‘Industry 4.0’ is significantly considered as the fourth industrial revolution [1], in which smart factories and intelligent manufacturing play a significant part. Besides new concepts of Internet of Things (IoT) [2], digital twins (DT) [3] and cloud manufacturing (CM) [4], the fundamental aspects of industry still heavily rely on traditional production procedures [5] such as casting, moulding, welding and machining. Since machining is vital for precision engineering and complex workpieces, much effort has been directed at improving the performance of NC machining. The quality of the milled surface affects the performance of the affiliated workpiece, since it greatly determines the precision of the geometry and duration of service time. To develop advanced manufacturing towards intelligent factories, surface quality prediction is of great research focus [6]. Comprehensive related approaches and studies have been reported on surface profile and the roughness of machined products [7, 8]. Generally, many features, such as cutting condition, tool status, material properties and process parameters (tool geometry, cut depth, feed rate and spindle) are considered to have a significant influence on the surface roughness. As the determination mechanism of surface roughness is complicated, no simple closedform model could accurately predict the surface finish.
Ending milling, which accounts for a large proportion of milling, is universally used in moulding, aerospace and automobile industries [9]. The surface quality is not only an important index to measure whether the workpiece meets the requirements but also the primary goal of monitoring the machining process and parameters’ optimisation. Therefore, it is essential to predict the quality before actual machining is performed, to decrease the time for boring parameter trials and corrections, and reduce the cost of the manpower. Lee et al. [10] proposed a highspeed milling surface roughness simulation approach, which adopted acceleration signals instead of cutting force signals for studying highspeed milling surface roughness. In the research, a statistical milling model was established for analysing the influence of spindle deformation and vibration on roughness. Mizugaki [11] and Kim [12], respectively, discussed the effect of the blunt radius of the blade on the surface roughness in the study of the tool path of the milling process. Then, Singh et al. [13] studied the bearing steel with higher hardness and used tools with different radii and bevel angles. The experimental results show that the feed rate has the most significant influence on the surface quality, while the bevel angle has the least influence on the machined surface. Quinsat et al. [14] believed that the processing strategy and parameters are related to the surface quality. The process parameters are obtained from the angle and the required surface quality, and the machining processing is simulated and tested. Results show that the importance of parameter design did achieve the required processing surface through parameters set strategy. Different cutting conditions make different influencing facts, and thus no closedform model could achieve accurate predicting, because different materials and different parameters, as well as different machine tools, can alter the cutting condition. Thus, direct statistical simulation or single effect analysis might not fulfil the requirement for predicting the surface quality.
Other researchers used evolutions, artificial intelligent algorithms or deep network for surface quality prediction. Zain et al. [15] used genetic algorithm to analyse the radial clearance angle of the milling cutter and considered the influence of feed and cutting depth on roughness, and finally found the optimal surface under the combination of high speed, low feed rate and radial clearance angle. Cosres et al. [16] used a noncontact displacement measurement system to record the movement of the tool during processing and the problem of tool vibration at high frequencies, and derived the surface topography after processing. Using traditional inspection equipment to inspect the surface quality of processed workpieces takes a lot of time, and it is impossible to predict the surface quality during processing. To be able to predict the surface quality during the machining process and adjust the machining process parameters in time to improve the machining quality, an intelligent detection method is urgently needed. Sahith Reddy Madara et al. [17] used an artificial neural network to model and predict surface roughness in abrasive waterjet cutting of Kevlar 49. Girish Kant et al. [18] developed an optimisation model by coupling the ANN and GA. In addition, evolution algorithm and artificial intelligence methods make great application prospects.
At present, in the machining process, various digital signals are generally obtained directly through sensors, but the collected data are always contaminated with noises, which seriously hinders the identification of the actual wear status of the tool, and thus could not reflect the surface quality. In this work, a modified convolutional recurrent neural network (CRNN) is applied to the prediction of surface quality. First, the validated features of milling force data in the machining process are extracted based on the proposed artificial network model. Then, a modified CRNN model is constructed by combining residual neural network and bidirectional long and shortterm memory as well as attention mechanism. The weight coefficients in the model are optimised according to the change of loss function and directional propagation principle, which greatly improves the effectiveness of the proposed model. Finally, the real experiment is carried out on a 5axis milling centre to validate the proposed approach.
Convolutional neural network (CNN) and recurrent neural network (RNN) are the main components of CRNN. CNN consists of multiple convolutional layers, pooling layers and fully connected layers. To deal with the enormous calculation, gradient loss and overfitting involved during the back propagation process, a rectified linear unit (ReLU) function will be used. This could provide rapid convergence speed. Then RNNs are adopted for modelling dynamic changes in time series. The details about classic CRNN can be found in Li et al. [19]; this study used CRNN for predicting combustion states of a rotary kiln. The classical CRNN architecture combines the advantages of deep CNN and RNN, and gives a good result; further, it shows that CRNN makes for a great application prospect. Also, CRNN network also has the characteristics of both CNN and RNN networks.
Due to the overfitting phenomenon in the deep learning network in CRNN in the feature extraction process, and the insufficient recognition of the fullposition context information by the convolutional network, based on the original CRNN, residual neural network, the bidirectional long and shortterm memory and attention mechanism are applied to build a modified CRNN model.
Most conventional CNN models pile up the convolutional layers to deepen the network to elevate the accuracy of the recognition. However, as the network structure deepens (resulting in redundancy of the convolutional layers), problems come to light. On the one hand, gradient loss or disappearance results in the inefficiency of updating the gradient to the previous network layers through back error propagation, causing parameters to not be updated. On the other hand, the model accuracy appears saturated and the accuracy declines rapidly, which means that the network degrades. The deep residual network is proposed to solve these problems. In this work, DenseNet is mainly introduced, discussed and applied to the CRNN framework. The CNN network performs well on discovering the local spatial features, while it cannot reflect the temporal relation information of the signals in time series.
The CRNN structure proposed in this paper aims to increase the depth of CNN network structure based on the framework of machining surface quality recognition algorithm, so as to improve its capability of deep feature extraction. Meanwhile, the structure of residual network is added to avoid the phenomenon of overfitting in the process of feature extraction of the deep network. At the same time, BILSTM and attention mechanism are combined to extract deep features, which makes up for the lack of a general convolutional network to recognise the complete location context information. Eventually, we integrate features through the fully connected layer and output the final status recognition result after softmax. In this paper, the machined surface quality is divided into three categories according to the value range of surface roughness value: good, medium and poor. The whole CRNN model framework is shown in Table 1.
The structure of modified CRNN
Convolution  5000  Conv 1*7, stride = 2 
Pooling  2500  Maxpool 1*3, stride = 2 
Dense Block 1  3000  (1*2 conv, 1*1 conv)*4 
Transition  3000  1*1 conv 
Block  1500  1*2 average pool, stride = 2 
BILSTM  725  BiLSTM, unit = 128 
Attention  725  Atten = 128 
Global pooling  128  Average pool 
Fully connect  64  Fully connected 
Output  3  Softmax 
The final network structure is shown in Figure 1. The inputs are threedirection cutting force signals. Since the sampling frequency in this experiment is 2500 Hz, the data collected in the experiment are enhanced through downsampling to obtain more data samples. Finally, the input dimension of the network is set as (10,000,1).
The input passes through the convolutional layer, pooling layer, DenseNet residual layer and BILSTM attention layer to complete the identification of machining surface quality. The structure of the whole network is shown in Table 1. The convolution kernel size is reduced, which can, on the one hand, improve the robustness of the network, and on the other hand, reduce the computational cost. Meanwhile, to adapt to the number of the output channels in the convolutional layer, a constant factor ranging (0,1) is added after the output of the dense block to adjust the number of output channels.
After the network structure is determined, the process of surface quality recognition based on CRNN has also been determined. First, the signal of the original milling force is downsampled to obtain the expanded data. Then, the data are normalised. Finally, the data are divided into training set and testing set with the ratio of 8:2, the training samples are input into the original CRNN network with four training control mechanisms and the training network enables it to have the fitting ability of machining surface quality recognition. An early stopping mechanism ensures the network will not overfit. Eventually, recognition ability and effect of the trained CRNN network are verified on testing set. The process flow of the model is shown in Figure 2.
After the prediction of the machining surface quality CRNN model and the training process, the weights in the model will be updated and optimised through the loss function and the principle of direction propagation, resulting in the gradual improvement of recognition ability. Figure 3 shows the changes of loss value and accuracy of the entire network in the training and testing sets. With the training process, loss value decreases continuously on both the training and testing sets, while the accuracy rate increases. Finally, the convergence is realised, and the prediction accuracy of the CRNN model on the verification set reaches 98.35%, which confirms the applicability and accuracy of the CRNN network proposed in this paper.
To verify the ability of the machining surface quality recognition and the effect of different CRNN deep networks, the DenseNet and BILSTM structure in CRNN deep network are separated and trained, respectively. The input is uniformly set as the force signal in the machining process, the output is set as three categories of surface quality and the test set is used for verification. The result of loss function on the testing set is shown in Figure 4, while the result of accuracy on testing set is shown in Figure 5. As is shown in Figures 4 and 5, in contrast with the rapid convergence and high accuracy of the prediction results of the CRNN, the loss of the DenseNet model on the testing set is more volatile, and the accuracy on the testing set is lower than that on the CRNN, although the DenseNet model can eventually converge. BILSTM is obviously not as effective at this task as the other two network structures.
According to the variation trend of loss value in Figure 5, it can be seen that DenseNet network can learn and extract the features of signals in the spatial domain, while BILSTM can extract the features of input signals in the temporal dimension and fit the correlation between various features through the attention mechanism. However, only these two parts of the network structure will cause the problem of insufficient model fitting ability, and thus it is necessary to combine the two effectively. The training results of the three networks are compared as shown in Table 2.
Comparison of prediction accuracy and operation time of different network
Proposed CRNN DenseNet(4_2) BILSTM  98.35% 97.68% 72.96%  15 18 22 
The proposed CRNN can learn more related characteristics compared with ordinary multilayer neural networks. At the same time, full correlation analysis is carried out on the extracted features through the BILSTM network with attention mechanism, so as to realise the accurate recognition of the machining surface quality. Based on the data in Table 2, the effectiveness of the proposed CRNN network on the surface quality prediction can be verified.
This work aimed to investigate the effect of cutting parameters and conditions on surface roughness parameters, such as cutting tool, stiffness of machine tool and material. In our experiment, the workpiece material was 42CrMo steel with a rectangular shape of 65 mm × 140 mm × 40 mm. The steel has good corrosion resistance and high hardness of 30 HRC. Therefore, its surface quality is challenging to guarantee during machining process. Table 3 shows the chemical composition of 42CrMo steel and Figure 6 shows the shape of the workpiece.
Workpiece material composition
0.38–0.43  0.15–0.35  0.75–1.00  ≤ 0.035  ≤ 0.040  0.80–1.10  0.15–0.25 
As shown in Figure 7, a series of dry milling experiments were conducted on Starrag LX051, which has a maximum of 18,000 rpm, rated torque of 181 Nm, positioning accuracy of 0.004 mm and repeat positioning accuracy of 0.002 mm. The cutting tool used for the experiments is a detachable end mill. The diameter of the shank is 16 mm. The insert on the shank is squareshouldered milling cutters (PKT11T7308PM). During milling, a Spike 1.2 rotary force measuring instrument was used to measure the threeway force. The roughness was measured by the SJ210 surface roughness tester, whose accuracy can reach 0.001 μm.
The orthogonal experiment method [20] is used to replace the enormous amount times of tests with only a partial part while still expressing the whole situation. This investigation is carried out upon surface roughness with different machining parameter combinations. To improve the experimental efficiency, this research work chooses the spindle speed, the axial cutting depth and the feed per tooth as the influencing factors, and each factor has three levels. Three levels were specified for each factor, as indicated in Table 4. The orthogonal array chosen was L7, which has seven rows corresponding to the number of parameter combinations, with three columns at three levels as shown in Table 5, in which A, B and C represent the machining parameters. The surface morphology of five groups is described in Table 6, and pictographic representation of the surface morphology is also provided in Figure 8.
Experiment factor and level
Spindle speed 
Cutting depth 
Feed per tooth 


3200  0.5  0.0625  
6400  1.5  0.125  
8000  2  0.25 
Designed orthogonal experiment
1  1  1  
1  2  2  
1  3  3  
2  1  2  
2  2  3  
2  3  1  
3  1  3 
Process parameters of cutting experiment samples
0.05  Figure 8(A)  0.567  
0.0625  Figure 8(B)  0.612  
0.125  Figure 8(C)  0.706  
0.2  Figure 8(D)  1.025  
0.25  Figure 8(E)  1.395 
The range of processed surface quality can be accurately predicted by the constructed deep network, and in real application scenarios, it is often necessary to accurately identify and predict the surface roughness more accurately, so as to accurately obtain the quality results of each process to ensure that each process is within the accuracy requirements. Based on the quality recognition model in the previous section, using the extracted internal features to build a regression model, mapping output to surface roughness value, that is, the input is the milling force signal during machining, and the output is the surface roughness prediction result. The specific process is shown in Figure 9. It involves replacing the softmax structure of the last layer of the CRNN network with a regression model to build a surface roughness prediction model during processing and using MSE mean square error loss function as objective function.
When conducting the surface roughness prediction experiment, since it is necessary to predict the quality of the workpiece during the entire processing process, the training and test sets need to use a complete processing experiment data individually, and the roughness prediction model in this section is based on the previous one. For the classification model in this section, the model parameters before the softmax layer of the model in the previous section are migrated as the trained weights. Only three sets of data are used to finetune the regression model. The experiment selects three sets of data of 1, 2 and 7 as the training set, and four sets of data of 3, 4, 5 and 6 as the test set to verify the prediction effect of the model. The abscissa represents the number of processing cycles, and the ordinate represents the surface quality value. The real surface quality value after secondary processing is used as the standard, and the result of comparison with the model output is shown in Figure 10.
The results show that even if there is a certain error between the model prediction and the real situation, the CRNN model proposed in this paper can meet the repeatability and accuracy requirements of the surface quality prediction in the general processing process.
A modified CRNN was proposed to predict the surface quality of end milling. The proposed CRNN network could solve the overfitting problem during the feature extraction process through optimisation of the convergence speed and loss function. The predicted values were compared with the actual experimental results, and the predicted values demonstrate a good accordance with the real cutting. Also, an accuracy rate of 98.35% could be achieved, which implies that, given our end milling circumstance, the experimental procedures adopted in the present study allowed us to predict the surface quality with higher precision and efficiency.
Experiment factor and level
Spindle speed 
Cutting depth 
Feed per tooth 


3200  0.5  0.0625  
6400  1.5  0.125  
8000  2  0.25 
Comparison of prediction accuracy and operation time of different network
Proposed CRNN DenseNet(4_2) BILSTM  98.35% 97.68% 72.96%  15 18 22 
Designed orthogonal experiment
1  1  1  
1  2  2  
1  3  3  
2  1  2  
2  2  3  
2  3  1  
3  1  3 
Process parameters of cutting experiment samples
0.05  0.567  
0.0625  0.612  
0.125  0.706  
0.2  1.025  
0.25  1.395 
Workpiece material composition
0.38–0.43  0.15–0.35  0.75–1.00  ≤ 0.035  ≤ 0.040  0.80–1.10  0.15–0.25 
The structure of modified CRNN
Convolution  5000  Conv 1*7, stride = 2 
Pooling  2500  Maxpool 1*3, stride = 2 
Dense Block 1  3000  (1*2 conv, 1*1 conv)*4 
Transition  3000  1*1 conv 
Block  1500  1*2 average pool, stride = 2 
BILSTM  725  BiLSTM, unit = 128 
Attention  725  Atten = 128 
Global pooling  128  Average pool 
Fully connect  64  Fully connected 
Output  3  Softmax 
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EnglishChinese CrossLanguage Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontaltorsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching A mathematical model of PCNN for image fusion with nonsampled contourlet transform Nonlinear Differential Equations in ComputerAided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with DiamondSquare Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Crossborder Ecommerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Timedelay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of watersaving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of AirConditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the winlose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on shortterm human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Crossborder Ecommerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edgebased finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of ecommerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leaderfollower model Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on ecommerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long shortterm memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSRAHP model A study of local smoothnessinformed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H_{2}N_{2} atmosphere Algorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Crossborder Ecommerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model ChineseEnglish Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model