# A Review of Thermal Error Modeling Methods for Machine Tools
## 4 Conclusions  
In the past ten years, more and more attention has been given to the research field of machine tool thermal errors. Some modeling methods such as LSSVM and neural network have performed well, but these type of models need many training samples and large number of calculations. It is easy to be invalidate in the process of adjusting weights, and they require a lot of time training samples, even with today's highly developed computer hardware technology. Therefore, there is not a blowout development of the research on neural networks or SVM. However, with the continuous development of computer hardware technology, neural networks and other modeling methods will surely show more possibilities. Traditional modeling methods such as least squares or multiple linear regression, etc. will not disappear completely for now. Because their mathematical principles are simple and the prediction performances are remarkable, models based on some improved algorithms still show strong vitality and have a place in engineering applications. Based on the discussion in the last section, the advantages and disadvantages should be considered for the use of thermal error modeling methods under different conditions. When the structure of the machine tool and working conditions are simple, LS and MRA should be considered first, and the prediction accuracy of MRA is generally higher. In contrast, NN and SVM are more suitable for complex machine tools and working conditions. If a single model cannot meet the requirement of accuracy and robustness, a hybrid model should be considered to solve this problem. In the future, research on the thermal error modeling technology of machine tools could be conducted in the following aspects. 1. On the premise of ensuring the prediction accuracy, the robustness of the thermal error model needs to be further improved. The established thermal error model under the same machine tool, specific working conditions, and environment has high accuracy. However, when the external environment, working conditions, instrument measurement accuracy, and other factors change, the prediction accuracy of the thermal error model will begin to deteriorate. 2. The current research on the thermal error of machine tools, from the selection of temperature measurement points, the establishment of the model, to the actual application of the compensation model, was all carried out on the same type of machine tool. However, when the model was transferred to other types of machine tools, the accuracy of the model was greatly compromised, or even completely invalid. Future research should consider whether the thermal error model can be successfully applied to different machine tools. 3. Besides the error compensation method, there is also the error prevention method to reduce the thermal error of machine tool. Considering that both of them have their own advantages and disadvantages in practical applications, how to combine the two reasonably to complement each other should become the content of future scholars' in-depth thinking and research. 4. The hybrid forecasting model is established based on two different mathematical modeling methods. By adjusting the weights of two methods, its performance can be improved. Compared with the single model, the hybrid forecasting model has a more comprehensive and stable error prediction performance for the machine tool. Under complex working conditions, it still has higher prediction accuracy. However, there are few studies on hybrid forecasting models, and the types of mathematical principles used in the hybrid model are limited to only two. In the future, a thermal error hybrid forecasting model based on three or more mathematical modeling methods may achieve unexpected performance. Conceptualization, Y.L. and W.W.; investigation, M.Y., Y.B. and Z.H. ; resources, M.Y., Y.B. and Z.H. ; writing--original draft preparation, Y.L., M.Y., Y.B. and Z.H. ; writing--review and editing, Y.L., M.Y., Y.B. and Z.H. ; supervision, Y.L. and W.W.; project administration, Y.L.