The Application of ANN and ANFIS Prediction Models for Thermal Error Compensation on CNC Machine Tools

Thermal errors can have significant effects on Computer Numerical Control (CNC) machine tool accuracy. The errors come from thermal deformations of the machine elements caused by heat sources within the machine structure or from ambient temperature change. The effect of temperature can be reduced by error avoidance or numerical compensation. The performance of a thermal error compensation system essentially depends upon the accuracy and robustness of the thermal error model and its input measurements. This thesis first reviews different methods of designing thermal error models, before concentrating on employing Artificial Intelligence (AI) methods to design different thermal prediction models. In this research work the Adaptive Neuro-Fuzzy Inference System (ANFIS) is used as the backbone for thermal error modelling. The choice of inputs to the thermal model is a non-trivial decision which is ultimately a compromise between the ability to obtain data that sufficiently correlates with the thermal distortion and the cost of implementation of the necessary feedback sensors. In this thesis, temperature measurement was supplemented by direct distortion measurement at accessible locations. The location of temperature measurement must also provide a representative measurement of the change in temperature that will affect the machine structure. The number of sensors and their locations are not always intuitive and the time required to identify the optimal locations is often prohibitive, resulting in compromise and poor results. In this thesis, a new intelligent system for reducing thermal errors of machine tools using data obtained from thermography data is introduced. Different groups of key temperature points on a machine can be identified from thermal images using a novel schema based on a Grey system theory and Fuzzy C-Means (FCM) clustering method. This novel method simplifies the modelling process, enhances the accuracy of the system and reduces the overall number of inputs to the model, since otherwise a much larger number of thermal sensors would be required to cover the entire structure. An Adaptive Neuro-Fuzzy Inference System with Fuzzy C-Means clustering (ANFIS-FCM) is then employed to design the thermal prediction model. In order to optimise the approach, a parametric study is carried out by changing the number of inputs and number of Membership Functions (MFs) to the ANFIS-FCM model, and comparing the relative robustness of the designs. The proposed approach has been validated on three different machine tools under different operation conditions. Thus the proposed system has been shown to be robust to different internal heat sources, ambient changes and is easily extensible to other CNC machine tools. Finally, the proposed method is shown to compare favourably against alternative approaches such as an Artificial Neural Network (ANN) model and different Grey models

A novel approach for ANFIS modelling based on Grey system theory for thermal error compensation

The fast and accurate modelling of thermal errors in machining is an important aspect for the implementation of thermal error compensation. This paper presents a novel modelling approach for thermal error compensation on CNC machine tools. The method combines the Adaptive Neuro Fuzzy Inference System (ANFIS) and Grey system theory to predict thermal errors in machining. Instead of following a traditional approach, which utilises original data patterns to construct the ANFIS model, this paper proposes to exploit Accumulation Generation Operation (AGO) to simplify the modelling procedures. AGO, a basis of the Grey system theory, is used to uncover a development tendency so that the features and laws of integration hidden in the chaotic raw data can be sufficiently revealed. AGO properties make it easier for the proposed model to design and predict. According to the simulation results, the proposed model demonstrates stronger prediction power than standard ANFIS model only with minimum number of training samples

A particle swarm optimisation-based Grey prediction model for thermal error compensation on CNC machine tools

Thermal errors can have a significant effect on CNC machine tool accuracy. The thermal error compensation system has become a cost-effective method of improving machine tool accuracy in recent years. In the presented paper, the Grey relational analysis (GRA) was employed to obtain the similarity degrees between fixed temperature sensors and the thermal response of the CNC machine tool structure. Subsequently, a new Grey model with convolution integral GMC(1, N) is used to design a thermal prediction model. To improve the accuracy of the proposed model, the generation coefficients of GMC(1, N) are calibrated using an adaptive Particle Swarm Optimisation (PSO) algorithm. The results demonstrate good agreement between the experimental and predicted thermal error. Finally, the capabilities and the limitations of the model for thermal error compensation have been discussed. Keywords: CNC machine tool, Thermal error modelling, ANFIS, Fuzzy logic, Grey system theory

A cuckoo search optimisation-based Grey prediction model for thermal error compensation on CNC machine tools

Purpose The purpose of this paper is to produce an intelligent technique for modelling machine tool errors caused by the thermal distortion of Computer Numerical Control (CNC) machine tools. A new metaheuristic method, the cuckoo search (CS) algorithm, based on the life of a bird family is proposed to optimize the GMC(1, N) coefficients. It is then used to predict thermal error on a small vertical milling centre based on selected sensors. Design/methodology/approach A Grey model with convolution integral GMC(1, N) is used to design a thermal prediction model. To enhance the accuracy of the proposed model, the generation coefficients of GMC(1, N) are optimized using a new metaheuristic method, called the CS algorithm. Findings The results demonstrate good agreement between the experimental and predicted thermal error. It can therefore be concluded that it is possible to optimize a Grey model using the CS algorithm, which can be used to predict the thermal error of a CNC machine tool. Originality/value An attempt has been made for the first time to apply CS algorithm for calibrating the GMC(1, N) model. The proposed CS-based Grey model has been validated and compared with particle swarm optimization (PSO) based Grey model. Simulations and comparison show that the CS algorithm outperforms PSO and can act as an alternative optmization algorithm for Grey models that can be used for thermal error compensation

The application of ANFIS prediction models for thermal error compensation on CNC machine tools

Thermal errors can have significant effects on CNC machine tool accuracy. The errors come from thermal deformations of the machine elements caused by heat sources within the machine structure or from ambient temperature change. The effect of temperature can be reduced by error avoidance or numerical compensation. The performance of a thermal error compensation system essentially depends upon the accuracy and robustness of the thermal error model and its input measurements. This paper first reviews different methods of designing thermal error models, before concentrating on employing an adaptive neuro fuzzy inference system (ANFIS) to design two thermal prediction models: ANFIS by dividing the data space into rectangular sub-spaces (ANFIS-Grid model) and ANFIS by using the fuzzy c-means clustering method (ANFIS-FCM model). Grey system theory is used to obtain the influence ranking of all possible temperature sensors on the thermal response of the machine structure. All the influence weightings of the thermal sensors are clustered into groups using the fuzzy c-means (FCM) clustering method, the groups then being further reduced by correlation analysis. A study of a small CNC milling machine is used to provide training data for the proposed models and then to provide independent testing data sets. The results of the study show that the ANFIS-FCM model is superior in terms of the accuracy of its predictive ability with the benefit of fewer rules. The residual value of the proposed model is smaller than ±4 μm. This combined methodology can provide improved accuracy and robustness of a thermal error compensation system

Thermal error modelling of a gantry-type 5-axis machine tool using a Grey Neural Network Model

This paper presents a new modelling methodology for compensation of the thermal errors on a gantry-type 5-axis CNC machine tool. The method uses a “Grey Neural Network Model with Convolution Integral” (GNNMCI(1, N)), which makes full use of the similarities and complementarity between Grey system models and artificial neural networks (ANNs) to overcome the disadvantage of applying either model in isolation. A Particle Swarm Optimisation (PSO) algorithm is also employed to optimise the proposed Grey neural network. The size of the data pairs is crucial when the generation of data is a costly affair, since the machine downtime necessary to acquire the data is often considered prohibitive. Under such circumstances, optimisation of the number of data pairs used for training is of prime concern for calibrating a physical model or training a black-box model. A Grey Accumulated Generating Operation (AGO), which is a basis of the Grey system theory, is used to transform the original data to a monotonic series of data, which has less randomness than the original series of data. The choice of inputs to the thermal model is a non-trivial decision which is ultimately a compromise between the ability to obtain data that sufficiently correlates with the thermal distortion and the cost of implementation of the necessary feedback sensors. In this study, temperature measurement at key locations was supplemented by direct distortion measurement at accessible locations. This form of data fusion simplifies the modelling process, enhances the accuracy of the system and reduces the overall number of inputs to the model, since otherwise a much larger number of thermal sensors would be required to cover the entire structure. The Z-axis heating test, C-axis heating test, and the combined (helical) movement are considered in this work. The compensation values, calculated by the GNNMCI(1, N) model were sent to the controller for live error compensation. Test results show that a 85% reduction in thermal errors was achieved after compensation

Thermal error modelling of machine tools based on ANFIS with fuzzy c-means clustering using a thermal imaging camera

Thermal errors are often quoted as being the largest contributor to CNC machine tool errors, but they can be effectively reduced using error compensation. The performance of a thermal error compensation system depends on the accuracy and robustness of the thermal error model and the quality of the inputs to the model. The location of temperature measurement must provide a representative measurement of the change in temperature that will affect the machine structure. The number of sensors and their locations are not always intuitive and the time required to identify the optimal locations is often prohibitive, resulting in compromise and poor results. In this paper, a new intelligent compensation system for reducing thermal errors of machine tools using data obtained from a thermal imaging camera is introduced. Different groups of key temperature points were identified from thermal images using a novel schema based on a Grey model GM (0, N) and Fuzzy c-means (FCM) clustering method. An Adaptive Neuro-Fuzzy Inference System with Fuzzy c-means clustering (FCM-ANFIS) was employed to design the thermal prediction model. In order to optimise the approach, a parametric study was carried out by changing the number of inputs and number of membership functions to the FCM-ANFIS model, and comparing the relative robustness of the designs. According to the results, the FCM-ANFIS model with four inputs and six membership functions achieves the best performance in terms of the accuracy of its predictive ability. The residual value of the model is smaller than ± 2 μm, which represents a 95% reduction in the thermally-induced error on the machine. Finally, the proposed method is shown to compare favourably against an Artificial Neural Network (ANN) model

Adaptive Neuro-Fuzzy Inference System integrated with solar zenith angle for forecasting sub-tropical photosynthetically active radiation

Advocacy for climate mitigation aims to minimize the use of fossil fuel and to support clean energy adaptation. While alternative energies (e.g., biofuels) extracted from feedstock (e.g., micro‐algae) represent a promising role, their production requires reliably modeled photosynthetically active radiation (PAR). PAR models predict energy parameters (e.g., algal carbon fixation) to aid in decision‐making at PAR sites. Here, we model very short‐term (5‐min scale), sub‐tropical region's PAR with an Adaptive Neuro‐Fuzzy Inference System model with a Centroid‐Mean (ANFIS‐CM) trained with a non‐climate input (i.e., only the solar angle, θZ). Accuracy is benchmarked against genetic programming (GP), M5Tree, Random Forest (RF), and multiple linear regression (MLR). ANFIS‐CM integrates fuzzy and neural network algorithms, whereas GP adopts an evolutionary approach, M5Tree employs binary decision, RF employs a bootstrapped ensemble, and MLR uses statistical tools to link PAR with θZ. To design the ANFIS‐CM model, 5‐min θZ (01–31 December 2012; 0500H–1900H) for sub‐tropical, Toowoomba are utilized to extract predictive features, and the testing accuracy (i.e., differences between measurements and forecasts) is evaluated with correlation (r), root‐mean‐square error (RMSE), mean absolute error (MAE), Willmott (WI), Nash–Sutcliffe (ENS), and Legates & McCabes (ELM) Index. ANFIS‐CM and GP are equivalent for 5‐min forecasts, yielding the lowest RMSE (233.45 and 233.01μ mol m−2s−1) and MAE (186.59 and 186.23 μmol m−2s−1). In contrast, MLR, M5Tree, and RF yields higher RMSE and MAE [(RMSE = 322.25 μmol m−2s−1, MAE = 275.32 μmol m−2s−1), (RMSE = 287.70 μmol m−2s−1, MAE = 234.78 μmol m−2s−1), and (RMSE = 359.91 μmol m−2s−1, MAE = 324.52 μmol m−2s−1)]. Based on normalized error, ANFIS‐CM is considerably superior (MAE = 17.18% versus 19.78%, 34.37%, 26.39%, and 30.60% for GP, MLR, M5Tree, and RF models, respectively). For hourly forecasts, ANFIS‐CM outperforms all other methods (WI = 0.964 vs. 0.942, 0.955, 0.933 & 0.893, and ELM = 0.741 versus 0.701, 0.728, 0.619 & 0.490 for GP, MLR, M5Tree, and RF, respectively). Descriptive errors support the versatile predictive skills of the ANFIS‐CM model and its role in real‐time prediction of the photosynthetic‐active energy to explore biofuel generation from micro‐algae, studying food chains, and supporting agricultural precision

Comparative study of ANN and ANFIS prediction models for thermal error compensation on CNC machine tools

Thermal errors can have significant effects on CNC machine tool accuracy. The errors usually come from thermal deformations of the machine elements created by heat sources within the machine structure or from ambient change. The performance of a thermal error compensation system inherently depends on the accuracy and robustness of the thermal error model. In this paper, Adaptive Neuro Fuzzy Inference System (ANFIS), Artificial Neural Network (ANN) and Particle Swarm Optimization (PSO) techniques were employed to design four thermal prediction models: ANFIS by dividing the data space into rule patches (ANFIS-Scatter partition model); ANFIS by dividing the data space into rectangular sub-spaces (ANFIS-Grid partition model); ANN with a back-propagation algorithm (ANN-BP model) and ANN with a PSO algorithm (ANN-PSO model). Grey system theory was also used to obtain the influence ranking of the input sensors on the thermal drift of the machine structure. Four different models were designed, based on the higher-ranked sensors on thermal drift of the spindle. According to the results, the ANFIS models are superior in terms of the accuracy of their predictive ability; the results also show ANN-BP to have a relatively good level of accuracy. In all the models used in this study, the accuracy of the results produced by the ANFIS models was higher than that produced by the ANN models

Application of GNNMCI(1, N) to environmental thermal error modelling of CNC machine tools

Thermal errors are often quoted as being the largest contributor to inaccuracy of CNC machine tools, but they can be effectively reduced using error compensation. Success in obtaining a reliable and robust model depends heavily on the choice of system variables involved as well as the available input-output data pairs and the domain used for training purposes. In this paper, a new prediction model “Grey Neural Network model with Convolution Integral (GNNMCI(1, N))” is proposed, which makes full use of the similarities and complementarity between Grey system models and Artificial Neural Networks (ANNs) to overcome the disadvantage of applying a Grey model and an artificial neural network individually. A Particle Swarm Optimization (PSO) algorithm is also employed to optimize the Grey neural network. The proposed model is able to extract realistic governing laws of the system using only limited data pairs, in order to design the thermal compensation model, thereby reducing the complexity and duration of the testing regime. This makes the proposed method more practical, cost-effective and so more attractive to CNC machine tool manufacturers and especially end-users