## 1 Introduction  
Environmental temperature has an enormous influence on large machine tools with regards to thermal error, which is different from the effect on ordinary-sized machine tools [1]. Thermal gradients cause heat to flow through the machine structure and result in non-linear structural error whether the machine is in operation or in a static mode [2]. It has been verified that thermally induced error accounts for 40%-70% of total errors [3; 4], and its effect on machine tools has become a well-recognized engineering problem in response to the increasing requirement of product quality [5]. As a result, reduction of thermal error is quite beneficial for a high-precision manufacturing system [6]. Besides, the coordinate offset is modified in the numerical control program according to the error value, so that the thermal error of the machine tool can be reduced. In the working cycle of a machine tool, the thermal errors are time-variant according to the change of environment and operating conditions. As far as most modeling methods are concerned, the thermal error models are all obtained by finding the best mapping relations between the thermal errors and some key temperature variables related to the heat source location [7]. [PERSON] [8] presented a novel approach in which a clustering method of temperature sensors was proposed, and the thermal error model of heavy machine tools was established. [PERSON] made a multiple regression analysis and proposed the artificial neural network model for the real-time forecast of thermal errors with numerous temperature measurements [9]. [PERSON] et al. presented a thermal modeling method based on independent component analysis to compensate for the thermal errors of a commercial machining center [10]. [PERSON] et al. [11; 12] proposed several methods to optimize the selection of minimum number of thermal sensors for machine tool thermal error compensation, such as ant colony algorithm-based back propagation neural network and synthetic grey correlation based grey neural network. [PERSON] et al. [13] proposed a hybrid thermal error modeling method to forecast the thermal expansion of a heavy boring and milling machine tool in \(z\)-axis. The thermal error prediction model mainly depends on the accuracy and robustness of the input temperature variables and the error of the machine tool system. [PERSON], et al. [14], utilized the inductive sensors array to measure the thermal error of a large gantry-type machine tool. [PERSON], et al. found a more reliable and practical measuring principal and method to monitor the deformation of heavy-duty Computer Numerical Control (CNC) machine tool structures using laser interferometer [15]. In addition, a novel temperature sensor, fiber Bragg grating (FBG) sensor, was used to collect the surface temperature of the machine [16]. [PERSON] designed a set of laser interferometer single-point tracking measuring method for thermal deformation of heavy machine tools [17]. In summary, thermal error predictive models for heavy-duty machine tools have been previously established and reported in the literature. However, two additional factors should be taken into account: (1) due to variation in the ambient environment and working conditions, thermal error of the concrete foundation should not be neglected [18; 19]; (2) in order to build accurate thermal error prediction model, it is necessary to build a neural network model with strong network feature extraction ability, generalization ability and network stability. To address these challenges, this paper proposes a self-organizing deep neural network (DNN) to improve the feature extraction capability and generalization ability of unsupervised training and to solve the problems of overfitting and lengthy training times. Deep neural network is one of the most commonly used tools in regression and prediction, and we propose that it could be a potential alternative to solve the particular problem in our domain.