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To accommodate the nonlinear and dynamic nature of thermal elastic process, Grey System Theory (GST) is adopted. By using this theory, GM (2, 1) and GM (1, 4) models are constructed. Real cutting experiment on a turning machine is conducted to establish and validate the model performance in terms of generalization ability. The comparison indicates that GM (2, 1) and GM (1, 4) perform better than other static and dynamic models such as Back Propagation Neural Network (BP) and Auto-regression Moving Average (ARMA). In addition, each of the two proposed model has their own advantages and they can be applied in practice.

The thermal error model of the 5-axis grinding machine tool was acquired by the homogeneous coordinate transformation, including 17 thermal error components. The thermal volumetric error real time compensation model was built by using the multiple regression analysis. The thermal error compensation control system and the temperature sensing system were developed and used as real-time compensation for the 5-axis grinding machine tool.

The extraction of pectin from sugar beet pulp by citric acid was carried out under different conditions using Box-Behnken design for four independent variables (pH, temperature, time and liquid to solid ratio). The yield of sugar beet pulp pectin ranged from 6.3% to 23.0%, and the content of protein from 1.5% to 4.5%. All independent variables significantly affected the yield, and all variables except liquid to solid ratio significantly affected the protein content. The yield increased as decreasing pH of extracting solution, extending time and advancing temperature, and an opposite relationship of effects between variables and content of protein was obtained. The chemical composition of collected samples was determined. Moreover, from the results of emulsifying properties study, the extracted pectin from sugar beet pulp could prepare steady oil-in-water emulsions. Therefore, it was inferred that the extraction conditions could influence yield and protein content, resulting in different emulsifying property.

In recent years, neural network (NN) modelling methods with different architectures and training strategies have been widely used in machine tool thermal error compensation field. Most of them are typically trial-and-error procedures in choosing the 'best network', while discarding all the rest. This paper introduces a new modelling method combining all of the trained NNs. This method is called optimal linear combination of neural networks (OLCNN), which can integrate the useful knowledge of the component NNs and thus improve model accuracy and generalisation ability (i.e., model robustness). Algorithms for selecting the component networks are presented after some associated critical issues are discussed. Real cutting experiments are conducted on a CNC turning machine to validate the effectiveness of the method. Analysis of different modelling conditions indicates that the best situation for using OLCNN is when the component networks are merely moderately trained. The modelling results show that significant improvement in the model accuracy and robustness is achieved comparing with single best NN and simple average of trained NNs. It is also applicable to hybrid different modelling methods other than NN.