FPK法在集总参数系统随机温度研究中的应用

Application of FPK method in the research on random temperature field of lumped system

应用FPK法研究了集总参数系统在对流和辐射环境下温度随机变化的规律. 设激励是均值为0的白噪声且系统参数为常量. 在与环境对流换热时,系统随机温度的均值不变,方差与系统时间常数的平方根成反比;在与环境辐射换热时,系统随机温度一般不呈正态分布,其中均值,均方值还与系统确定性温度有关. 由此可知,当存在随机激励时,用有热惯性的测温系统精确测定动态温度是不可能的.

An analytical study of random temperature of lumped system by FPK method, under the boundary condition of heat convection and radiation is carried out in the paper. The random temperature excitation is assumed to be white noise with zero-mean value and the system time constant is supposed to be a constant. Under the boundary condition of heat convection, the random temperature of system obeys normal distribution. The mean of random temperature of system is zero, and the variance is inversely proportional to square root of timeconstant. Under the boundary condition of radiation, the random temperature of system does not obey normal distribution. When applying the above theory to temperature measurement by thermocouple, the random variation of thermocouple temperature relates to the time constant. The precise measurement of dynamic temperature is impossible when there is random excitations.