^{1}

^{2}

^{3}

^{1}

^{2}

^{3}

^{1}

^{2}

^{3}

^{1}

^{2}

^{3}

^{1}

^{2}

^{3}

^{4}

^{1}

^{2}

^{3}

^{4}

The prediction model is the most important part of the virtual metrology system. Predicting the performance of the machining process has been widely applied in manufacturing, which can reduce costs and improve efficiency compared with the manual operation. In this paper, a novel performance prediction model for the machining process is proposed based on the interval type-2 fuzzy neural network. The interval type-2 fuzzy logic system with a complete rule base, type-reduction, and defuzzified output is simplified by the BMM method to meet the requirements of the prediction. The proposed prediction model is trained using a gradient-based optimization algorithm. To evaluate the performance of the proposed approach, it is applied to wire electrical discharge turning process for predicting material removal rate and surface roughness with a published dataset. The results show that the proposed method is an effective scheme in the studied cases.

The main objective in the machining process is the improvement of the product quality and productivity at the same time. In order to ensure that product quality meets the requirements, the machining quality inspection of multiple key parts is an essential link in the production process. However, it is almost impossible to perform the total inspection for all parts in real manufacturing processes because such an inspection takes remarkable time and imposes an undeniable delay in the quality control. Although the quality in this method is guaranteed, the continuity of the production is adversely affected. In the context of intelligent manufacturing, finding novel intelligent detection methods is highly required. Reviewing the literature indicates that several schemes have been proposed in this area so far. More specifically, the virtual metrology technology is an effective scheme to perform the quality process monitoring. Investigation and implementation of the virtual metrology have increasingly attracted attentions from both academia and industry. Studies show that this method can effectively reduce the detection time and achieve the total inspection of the product quality. The virtual metrology has been widely applied in diverse high-tech industries, including the semiconductor industry [

In recent years, different modelling techniques in prediction of machining performances have been proposed for various processes. Because of the causal relationship between machining process and performances, machining process parameters and performances are often used as input and output for modelling, respectively. Due to complexity and uncertainty of the machining processes, soft computing techniques are being preferred to physics-based models for predicting the performance of the machining processes and optimizing them. A review of application of soft computing techniques in machining performance prediction and optimization has been presented [

Depending on the types of data and the information characteristics of the interested systems, prognosis techniques can be classified into three main categories, including the physics-based, data-driven, and model-based techniques [

Abnormal machining condition causes quality loss in the finished parts. To this end, Lu et al. [

Interval type-2 fuzzy neural networks (IT2FNN) combine the reasoning ability of the interval type-2 fuzzy logic system (IT2FLS) and the self-learning ability of the neural network so that it is a powerful scheme in dealing with the uncertain and nonlinear problems. Although the IT2FNN method has been widely applied in diverse fields, it has been rarely applied in the machining. Type-2 fuzzy logic estimation provides a possibility to show uncertainties in the manufacturing process and can automate the process monitoring, which is of significant importance in maintaining the high quality production. Chen and Vachtsevanos [

Wire electrical discharge machining (WEDM) is a widely accepted material removal process for components with intricate shapes and profiles. Moreover, wire electrical discharge turning (WEDT) is an emerging area and it can be used for generating cylindrical forms on difficult-to-machine materials by adding a rotary axes on the WEDM. The WEDT process can be modelled through the artificial neural network with feedforward backpropagation algorithm and ANFIS [

In the present study, it is intended to present a novel prediction model based on the simplified interval type-2 fuzzy neural network for predicting the MRR and Ra in the WEDT, which are important for increasing the productivity and quality of the products. To this end, the IT2FNN method with a complete rule base and the BMM method will be applied to simplify the type-reduction and defuzzified output of the IT2FLS.

The remainder of this article is organized as follows. Structure of the interval type-2 fuzzy neural network and parameters of the learning algorithm are presented in Section

In this section, it is intended to introduce the structure of the simplified IT2FNN method. With no loss of generality, multiple-input multiple-output (MIMO) fuzzy systems can be decomposed into a series of multiple-input single-output (MISO) fuzzy systems. Figure

Structure of the interval type-2 fuzzy neural network.

In the present study, an interval type-2 fuzzy logic system is considered with a complete rule base, and the consequent parts of the rules are of the Takagi–Sugeno–Kang (TSK) type. In this case, the

The specific expression of each layer is discussed as follows.

Layer 1 (the input layer): this layer contains

Layer 2 (the membership function layer): in this article, the Gaussian primary membership function (MF) with uncertain standard deviation and fixed center value is applied in the interval type-2 fuzzy set

where

Then, the output of each node can be represented as an interval

Layer 3 (the rule layer): this layer contains

Layer 4 (the normalization layer): the number of neurons in this layer is also

Layer 5 (the type-reduction layer): the outputs of this layer can be obtained by the firing nodes and the connecting weight vectors, which are defined in the form below:

where

Layer 6 (the output layer): each node in this layer computes the output variable through the defuzzification operation. The output value of this layer can be expressed in the form below:

Distribution of the interval type-2 membership function with uncertain standard deviation.

In this section, it is intended to use the gradient descent method to derive the parameter learning of the IT2FNN system. For clarification, a single-output system is studied to minimize the objective error. The error function is defined as follows:

Therefore, the parameters of the updated law equation can be rewritten as follows:

Then, consequent parameters used in the layer 4 are tuned by the following equations:

Antecedent parameters used in layer 2 are tuned as follows:

Partial derivatives in the foregoing expressions can be expressed as follows:

It is worth noting that the parameter

An important issue for each learning algorithm is the convergence. The convergence of the gradient descent method depends on the selection of the initial value for the learning rate. The convergence is guaranteed when the following inequality is satisfied [

In this section, it is intended to evaluate the performance of the proposed method in predicting the MRR and Ra in the WEDT. The experimental dataset in this paper is published in [

Datasets for designing the experiment [

No. | Pulse off-time ( | Spark gap ( | Servo feed (level) | Rotational speed (rpm) | Flushing pressure (bar) | MRR (mm^{3}/min) | Ra ( |
---|---|---|---|---|---|---|---|

1 | 30 | 30 | 3 | 30 | 3.267 | 1.24 | 2.396 |

2 | 30 | 50 | 5 | 70 | 3.267 | 2.21 | 3.756 |

3 | 30 | 80 | 8 | 100 | 3.267 | 2.60 | 4.134 |

4 | 34 | 30 | 5 | 100 | 3.267 | 1.73 | 3.172 |

5 | 34 | 50 | 8 | 30 | 3.267 | 3.78 | 5.009 |

6 | 34 | 80 | 3 | 70 | 3.267 | 1.45 | 2.827 |

7 | 42 | 30 | 8 | 70 | 3.267 | 1.50 | 2.899 |

8 | 42 | 50 | 3 | 100 | 3.267 | 0.95 | 2.116 |

9 | 42 | 80 | 5 | 30 | 3.267 | 1.68 | 3.133 |

10 | 30 | 30 | 3 | 30 | 1.893 | 1.16 | 2.311 |

11 | 30 | 50 | 5 | 70 | 1.893 | 2.20 | 3.539 |

12 | 30 | 80 | 8 | 100 | 1.893 | 2.47 | 4.003 |

13 | 34 | 30 | 5 | 100 | 1.893 | 1.40 | 2.694 |

14 | 34 | 50 | 8 | 30 | 1.893 | 3.72 | 4.897 |

15 | 34 | 80 | 3 | 70 | 1.893 | 1.37 | 2.502 |

16 | 42 | 30 | 8 | 70 | 1.893 | 1.46 | 2.895 |

17 | 42 | 50 | 3 | 100 | 1.893 | 0.82 | 2.069 |

18 | 42 | 80 | 5 | 30 | 1.893 | 1.65 | 3.124 |

19 | 30 | 30 | 3 | 30 | 1.263 | 1.10 | 2.264 |

20 | 30 | 50 | 5 | 70 | 1.263 | 1.48 | 2.860 |

21 | 30 | 80 | 8 | 100 | 1.263 | 2.22 | 3.794 |

22 | 34 | 30 | 5 | 100 | 1.263 | 1.34 | 2.506 |

23 | 34 | 50 | 8 | 30 | 1.263 | 3.20 | 4.576 |

24 | 34 | 80 | 3 | 70 | 1.263 | 1.35 | 2.520 |

25 | 42 | 30 | 8 | 70 | 1.263 | 1.37 | 2.588 |

26 | 42 | 50 | 3 | 100 | 1.263 | 0.78 | 2.048 |

27 | 42 | 80 | 5 | 30 | 1.263 | 1.54 | 2.987 |

28 | 30 | 50 | 8 | 70 | 3.267 | 2.80 | 4.281 |

29 | 34 | 80 | 5 | 50 | 1.893 | 1.44 | 2.744 |

30 | 42 | 50 | 3 | 50 | 1.263 | 0.98 | 2.149 |

MRR and Ra are separately predicted through the proposed IT2FNN scheme. In this regard, the IT2FNN architecture factors are presented in Table

Design factors in the IT2FNN architecture.

Parameter | MRR | Ra |
---|---|---|

Layer 1: Number of input nodes | 5 | 5 |

Layer 2: Number of membership functions | 10 | 10 |

Layer 3: Number of rules | 32 | 32 |

Layer 4: Number of normalization nodes | 32 | 32 |

Layer 5: Number of type-reduction nodes | 2 | 2 |

Layer 6: Number of output nodes | 1 | 1 |

Footprint of uncertainty | Gaussian with uncertain standard deviation | Gaussian with uncertain standard deviation |

In the present study, the first 27 data among 30 sets of experimental data are used for training, while the last 3 ones are considered for testing. It should be indicated that process parameters, which were previously discussed in Section

Figures

IT2FNN training process and prediction results for MRR.

IT2FNN training process and prediction results for Ra.

Obtained results show that, after 200 training iterations, the RMSE approached to its asymptotic value and obtained outputs from the model match with the actual measured results during the training so that the prediction accuracy of the test samples increases. Furthermore, it is found that the proposed model has a good generalization ability. Table

Obtained results from different schemes.

NO. | Experimental results | Prediction result of ANN [ | Prediction result of ANFIS-GA [ | Prediction result of ANFIS-MGA [ | Prediction result of IT2FNN | |||||
---|---|---|---|---|---|---|---|---|---|---|

MRR | Ra | MRR | Ra | MRR | Ra | MRR | Ra | MRR | Ra | |

28 | 2.80 | 4.281 | 2.46 | 3.734 | 2.48 | 3.78 | 2.644 | 3.894 | 2.7797 | 4.2299 |

29 | 1.44 | 2.744 | 1.32 | 2.599 | 1.36 | 2.874 | 1.549 | 2.979 | 1.4631 | 2.8612 |

30 | 0.98 | 2.149 | 0.92 | 2.552 | 1.03 | 1.791 | 0.925 | 2.138 | 0.9451 | 2.2544 |

0.2110 | 0.4011 | 0.1926 | 0.3633 | 0.1144 | 0.2615 |

Studies show that predicting the performance of the machining process is of great significance in the intelligent manufacturing. In practical applications, the precision and the efficiency of the predicting model are two key factors. Obtained results in the present study demonstrate that the IT2FNN is a powerful scheme in dealing with uncertain and nonlinear problems, which is beneficial to predict the performance of the machining process. The proposed method has been used to predict the material removal rate and surface roughness in the wire electrical discharge turning process, which improves the efficiency and precision compared with the related research results. In the near future, it is intended to apply this method for virtual metrology of the machining precision in other machining process fields.

The data used to support the findings of this study are included within the article.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This research was supported by the National Key R&D Program of China (Grant no. 2018AAA0101802).