In addition to Beck inverse algorithm, regularization method and optimization method are also the methods that researchers focus on.
Tikhonov et al. Obtained the objective function for solving the heat transfer coefficient of casting die interface in solidification process according to the regularized universal function, which is the regularization method for calculating the heat transfer coefficient of casting die interface. Sui Dashan et al. Studied the heat transfer behavior of casting mold interface based on regularization method, and discussed the stability of parameter identification in various algorithms. Dong et al. Used regularization method to study the interface heat transfer behavior between Ni based superalloy and shell during investment casting.
The core idea of the optimization method is that the solution of the heat transfer coefficient of the casting die interface, a typical inverse problem, is equivalent to the optimization problem of the square sum of the difference between the measured temperature and the calculated temperature as the objective function. RANJBAR et al. Obtained the interface heat transfer coefficient of Sn Pb alloy casting die by optimization method. In addition, loulou et al. Used this method to estimate the interfacial heat transfer coefficient between the metal droplet and the substrate during the chilling process. In addition, some non gradient optimization methods have attracted the attention of researchers, such as genetic algorithm, neural network algorithm, particle swarm optimization, quadratic programming algorithm and so on.
Das et al. Studied the effect of spatial variation on the interfacial heat transfer coefficient by using the boundary element method. However, it is difficult for this method to deal with the nonlinear problem of the physical parameters of castings and molds, which limits the application of this method.
In recent years, the application of stochastic probability model to inverse algorithm, especially the application of Bayes posterior probability model to inverse algorithm, has been widely concerned by researchers. Assuming that the measured temperature conforms to Gaussian distribution, the above probability model is used to maximize the probability distribution of the measured temperature, which is similar to the least square method. One of the great advantages of applying these probabilistic models to the inverse algorithm is that the uncertainty of the initial input temperature parameters can be considered. In this case, the model can still obtain accurate results. However, a big disadvantage of this method is that it has a large amount of calculation, which is extremely unfavorable for large-scale or large-scale data processing, so its application is greatly limited, and it is still in the research state.
Compared with other methods, Beck algorithm improves the stability of back calculation by using multiple future time steps. Because the current heat flow has an impact on the temperature at all subsequent times, it is better to select multiple future time periods for the inverse calculation than only using the current time temperature. Through in-depth analysis of the characteristics of the inverse calculation process, it is found that using multiple future time steps can ensure the stability and accuracy of the calculation results. Beck’s method solves the sensitivity of the back calculation process to the initial temperature error, which has been widely used.