两个数学建模问题的探讨

探讨了两个在教科书中作为例题的数学建模问题，一个是关于渔业生产的，另一个关于体育训练，对于前者，提出一个更为合理的解法；对于后者，则提出其中数学推导上的错漏并得出新的结论。     

磁粉制动器的滑差功率研究

首先用理论方法对经过结构优化的磁粉制动器的滑差功率进行了计算，然后在自行设计、安装的实验台上对其进行了温升实验，所得理论计算值和实测值的一致性较好，在此基础上确定了它的额定滑差功率线图。     

自然伽玛曲线上的“海侵针”及其地质意义

自然伽玛曲线上的尖锥状～针状特高异常—“海侵针”,常可指示海侵作用与海相层的存在:“阵发式”海退与“振荡式”海退则是含煤岩系形成过程中两类常见的利于聚煤的海退类型.     

Internal interactions within the human circadian system: the masking effect

Summary In the realm of human circadian rhythms, the masking effect is defined as the change in the course of deep body temperature induced by changes in the degree of physical activity, or by the alteration between sleep and wake. This effect is particularly obvious during internal desynchronization where the rhythms of deep body temperature, and the sleep-wake sleep-wake sleep cycle — i.e. one of the masking factors — run with different periods.Every sleep onset is accompanied by a rapid drop, and wake onset by a rapid rise in deep body temperature, each one with an overshoot of about 50% of the steady state variations. When rhythms are calculated, with the dominant temperature period as the screening period, exclusively from data obtained during sleep episodes, on the one hand, and from those obtained exclusively during wake, on the other, two average cycles emerge: the sleep temperature curve and the wake temperature curve. Both run in parallel but are separated by the masking effcct. As derived from many experiments, the mean masking effect amounts to 0.28±0.06°C. The masking effect also depends to some extent on the phase of the temperature rhtthm; it is larger than average around the temperature maximum and during the descending phase of the temperature cycle, where the alertness commonly is highest and the probability to sleep, in general, and the REM sleep propensity, in particular, are smaller than average. This also can be interpreted to indicate that the sleep temperature curve is phase advanced relative to the wake temperature curve; this, on the average, by 0.9±0.3 h.If the individually determined amount of masking is added to the temperature data obtained during sleep, or substracted from the temperature data obtained during wake, a temperature curve emerges that can be though of as being purified of the masking effect. Analyses of this artificial curve allow estimation of that part of the internal interactions uninfluenced by the masking effect. On the average, about half of the amount of interaction between the rhythm of sleep-wake and that of deep body temperature is explained by the masking effect, whereas the other half is oscillatory interaction. Both types of interaction are inherent and inseparable parts of the circadian clock mechanism, as can be deduced from model considerations.     

考虑应力集中的吊车梁多轴疲劳寿命预测

钢结构吊车梁在工业建筑中被广泛应用,应力集中的存在导致几何不连续位置在复杂应力下服役.借助有限元法分析吊车梁应力-应变状态,确定危险点位置,并提取应力、应变分量;以应变能密度作为损伤参量并以最大平面为临界面,基于能量准则建立临界面位置数值计算方法,结合有限元结果给出吊车梁临界面位置;考虑吊车梁在非对称载荷下服役,借助Goodman方程进行平均应力修正,并结合Q355D钢近似S-N曲线计算疲劳寿命.该方法考虑了应力集中处多轴应力对疲劳损伤的影响,可以为复杂应力下几何不连续钢构件的疲劳寿命评估提供新方法.     

关于纺织机械噪声评价标准的探讨

机器噪声的污染问题,日益受到世界各国的重视和关注,现在国际上对机器噪声的测量,主要采用声功率级。但用这种声功率级的评价指标尚有某些不足之处,本文拟在声功率级基础上,提出“机器噪声相对声功率系数”的概念,作为评价、比较、改进机器噪声及综合质量的补充指标,以弥补声功率级的不足。     

扩展裂纹缺陷评定方法的优化研究

裂纹扩展的缺陷评定方法,越益受到了人们的重视,美国ＥＰＲＩ提出的“裂纹 推力图”方法,虽然准确合理,但方法偏于繁复,尚难于向工程界推广。清华大学力学 研究所曾先后提出几种评定方法,以期使评定过程得以简化。在此基础上,文章提出 “相容应力增量”法作为优化方法,它将使全部评定过程大为简化,从而为扩展裂纹的 缺陷评定方法向工程界推广创造便利条件。     

光伏模组积灰与阴影特性分析及识别方法

针对光伏模组积灰与阴影特性识别问题,详细分析了积灰和阴影的光伏特性曲线差异,揭示了阴影光伏曲线的拐点时变特性。提出由特性曲线的拐点数量及电流电压特性条件共同构成训练模型的输入特征量,基于CatBoost算法训练积灰和阴影识别模型。最后,利用光伏模组实测数据对CatBoost算法、ID3和GA-BP算法训练出的识别模型进行性能分析和对比测试,结果表明基于CatBoost训练出的识别模型输入量区分性强、诊断精度高,极具工程应用价值。     

一般生长曲线模型中共同均值参数的线性估计的泛容许性

本文对于一般生长曲线模型中共同均值的线性估计的可容许性。     

关于人造天体运动轨迹确定的一种方法

作者在该文中,从万有引力定律出发,根据有心力的特点,再采用切坐标法很方便地推导出在地球万有引力作用下,人天体运动的轨道必是圆锥曲线,并指出由发射时初始条件能方便地进一步确定其轨迹的形状。