###### Abstract
In comparison with the LS method, there are more independent variables in the MRA model [12]. It is more effective and practical to use the optimal combination of several independent variables to predict the dependent variables. Hence, the model of thermal error established through MRA method brings about higher precision and stronger robustness. However, when involving massive variables, the computation of MRA method is time-consuming and the correlation between thermal errors and temperature variables is merely taken into account, which will result in the coupling of temperature variables and reduce the precision of the model. The modeling method based on GS theory is simpler and independent of the massive data information [13]. The problem of using GS theory for thermal error modeling is that the model predicts self-development on the basis of its own raw data. As a result, picking altered data from the primary data series will make a big difference to the model. The SVM method that possesses excellent capability in nonlinear fitting [14] is deemed to be an appropriate model for predictive learning in small samples. However, it is hard to optimize the selection of parameters when utilizing SVM method for thermal error modeling. Moreover, the solving process is resource-consuming and slow. Generally speaking, neural network has advantages over LS and MRA in the predictive accuracy. There are two common neural network methods: back propagation (BP) and radial basis function (RBF). BP neural network can be used to completely approximate complex nonlinear relations, which contributes to its wide application in thermal error modeling [15]. However, BP neural network has a slow convergence rate and is liable to descend into the local extremum. Furthermore, the initial value is also hard to determine. As a feedforward neural network, RBF neural network has simple structure and good performance in approximation and global optimization [16]. However, compared with BP neural network, its key feature function is hard to be extracted and its generalization capability is poor. In order to optimize the initial structural arguments of RBF neural network, particle swarm optimization (PSO) algorithm is adopted because it can iteratively update and change the moving direction of particles to seek optimal solution. PSO algorithm, that is one of the most commonly used metaheuristics in process optimization, has high computational efficiency and requires less adjustment of parameters. As a result, it is considered as a random optimization algorithm with high robustness, and is widely used in function optimization [17; 18], neural network training [19; 20], fuzzy system control [21; 22], and other applications of genetic algorithms [23; 24; 25]. However, due to the lack of sophisticated search methods, PSO algorithm often cannot get accurate results or guarantee convergence to the global optimum. In order to overcome the premature convergence of PSO algorithm and other related algorithms mentioned above, an improved PSO-RBF neural network (IPSO-RBFNN) model is proposed for thermal error prediction of machine tools in this paper. In this model, compression factors are used to effectively control the particle velocity and balance the solutions between local and global search. Based on the improved PSO algorithm, the initial structural arguments of RBF neural network are optimized. It turns out that the IPSO-RBFNN model for thermal error prediction has better predictive performance. The following is the organizational structure of the rest of the article. Literature review for this study is presented in Section 2. The thermal error experiment on a 5-axis CNC machine tool, named as DMG-DMU65, is described in Section 3. The technical specifics of the IPSO-RBFNN model are provided in Section 4. The comparisons of the IPSO-RBFNN model with other models on the basis of the experimental data are conducted in Section 5.