The probability density function of the multidimensional Gaussian distribution is used as the fitting function of the surface heat source temperature
The Gaussian probability density function of any NN-dimensional random variable can be derived from the probability density function of a multi-dimensional independent random variable. For example, let y=A(x−μ)y=A(x−μ), use μμ for translation, and matrix AA for correlation transformation . The probability density function of the NN dimension Gaussian distribution is as follows f(x)=(2π)−N2|Σ|−12exp −12(x−μ)TΣ−1(x−μ) (6)f(x)=(2π) −N2|Σ|−12exp[−12(x−μ)TΣ−1(x−μ)]
where μμ represents the mean vector and ΣΣ represents the covariance matrix. The exponent part can be written in another form: L=−12(x−μ)TΣ−1(x−μ)=−12(xTΣ−1x−2μTΣ−1x+μTΣ−1μ) or the Coldak heat source model can be used to use these two Model to fit the function model to establish the heat transfer equation (find the relationship between the time, temperature in the temperature zone, and the center temperature of the welding zone) to fit the model to fit the data, bring out the unknown quantity and consider the process limit given by the problem, Fitting the normal distribution function