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Prediction of surface roughness based on a hybrid feature selection method and long short-term memory network in grinding

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Abstract

Ground surface roughness is regarded as one of the most crucial indicators of machining quality and is hard to be predicted due to the random distribution of abrasive grits and sophisticated grinding mechanism. In order to estimate surface roughness accurately in grinding process and provide feasible monitoring scheme for practical manufacturing application, a novel prediction system of surface roughness is presented in this article, including the processing of grinding signals, selection of feature combination, and development of prediction model. Grinding force, vibration, and acoustic emission signals are collected during the grinding of C-250 maraging steel. Numerous features in time domain and frequency domain are extracted from original and decomposed signals. A hybrid feature selection approach is proposed to select features based on their relevance to surface roughness as well as hardware and time costs. A sequential deep learning framework, long short-term memory (LSTM) network, is employed to predict ground surface roughness. The results have shown that the LSTM model achieves excellent prediction performance with a feature combination of grinding force and acoustic emission. After considering the hardware and time costs, features in acceleration signal replace those in grinding force and acoustic emission signals with slight loss of prediction performance and significant reduction of costs, which proves the practicability and feasibility of proposed prediction system.

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Funding

This work is supported in by the Shanghai Sailing Program (19YF1401400).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Weicheng Guo & Zishan Ding

  2. College of Mechanical Engineering, Donghua University, Shanghai, 201620, China

    Chongjun Wu & Qinzhi Zhou

Authors
  1. Weicheng Guo
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  2. Chongjun Wu
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  3. Zishan Ding
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  4. Qinzhi Zhou
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Contributions

Weicheng Guo designed and carried out the grinding experiment, analyzed the data, and drafted the manuscript. Chongjun Wu anticipated the experiment and measured the surface roughness. Zishan Ding revised the manuscript. Qinzhi Zhou provided the experimental and testing equipment.

Corresponding author

Correspondence to Weicheng Guo.

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Appendix

Appendix

According to Fig. 9 and Table 2, the scale scores of hardware cost CH and time cost CT in the total cost C are 1 and 5, respectively, which means that the importance of CH is greater than CT since the hardware cost is prior to the computation time in industrial applications. The pairwise comparison matrix of the total cost C can be expressed as

$$ {A}^C=\left[\begin{array}{cc}1& 5\\ {}1/5& 1\end{array}\right] $$
(21)

The purchase cost \( {C}_p^H \) and installation cost \( {C}_i^H \) in the hardware cost of the criteria level can be expressed as 1 and 3, respectively, which means that the purchase price of a sensor is a more important consideration compared with its installation method. The pairwise comparison matrix of hardware cost CH can be expressed as

$$ {A}^{C^H}=\left[\begin{array}{cc}1& 3\\ {}1/3& 1\end{array}\right] $$
(22)

The sub-criteria in Fig. 9 determines the priorities of dynamometer, accelerometer and AE sensor with respect to the purchase cost \( {C}_p^H \) and installation cost \( {C}_i^H \). The purchase cost of dynamometer, accelerometer, and AE sensor ranges from hundreds to ten thousands of dollars. Therefore, if the scale score of the price of dynamometer ($50,000, including charge amplifier) used in this article is 1, then the scale scores of the price of accelerometer ($400) and AE sensor ($2500, including pre-amplifier) are 1/9 and 1/7, respectively. The pairwise comparison matrix of purchase cost \( {C}_p^H \) can be expressed as

$$ {A}^{C_p^H}=\left[\begin{array}{ccc}1& 1/9& 1/7\\ {}9& 1& 2\\ {}7& 1/2& 1\end{array}\right] $$
(23)

The dynamometer is more cumbersome to install than accelerometer and AE sensor and requires specific clamps designed for mounting on the worktable, while accelerometer and AE sensor can be attached on the workpiece or fixture simply by magnetic cases. Therefore, if the scale score of the installation cost of dynamometer is 1, then the scale scores of the installation cost of accelerometer and AE sensor are 1/5 and 1/5, respectively. The pairwise comparison matrix of installation cost \( {C}_i^H \) can be expressed as

$$ {A}^{C_i^H}=\left[\begin{array}{ccc}1& 1/5& 1/5\\ {}5& 1& 1\\ {}5& 1& 1\end{array}\right] $$
(24)

The time cost CTof different types of signal features can be obtained from their computation times, as shown in Table 9. The computation time includes signal processing time and feature extraction time. These two steps were executed on a laptop with i7-6820HQ CPU @2.7GHz and 16GB DDR4 RAM.

Table 9 Computation time of different types of signal features
Full size table

Comparing each row in Table 9, it can be seen that whether it is a grinding force, vibration, or AE signal, the time- and frequency-domain features in the original signal are always calculated in the least amount of time, followed by the time- and frequency-domain features in the WPD signal, while the time- and frequency-domain features in the EEMD signal are calculated in the longest amount of time. Thus, if the scale score of the time cost of time-domain features in the original signals is 1, then the scale scores of the time cost of frequency-domain features in the original signals, time-domain features in the WPD signals, frequency-domain features in the WPD signals, time-domain features in the EEMD signals, and frequency-domain features in the EEMD signals are 2, 2, 3, 8, and 9, respectively. Then, the pairwise comparison matrix of time cost CT can be expressed as

$$ {A}^{C^T}=\left[\begin{array}{cccccc}1& 2& 2& 3& 8& 9\\ {}1/2& 1& 1& 2& 7& 8\\ {}1/2& 1& 1& 2& 7& 8\\ {}1/3& 1/2& 1/2& 1& 6& 7\\ {}1/8& 1/7& 1/7& 1/6& 1& 2\\ {}1/9& 1/8& 1/8& 1/7& 1/2& 1\end{array}\right] $$
(25)

Similarly, the effect of the sensor type in sub-criteria level on the computation time of the time-domain and frequency-domain features can be estimated by each of the columns in Table 9. The computation time for features in the grinding force and acceleration signals is almost the same, while the computation time for features in the AE signal is several times longer than force and acceleration signal features. The pairwise comparison matrices of time costs for force, acceleration, and AE signal features can be constructed by the multiples of the time and are presented in Eqs. 26, 27, 28, 29, 30, and 31.

$$ {A}^{C_{o-t}^T}=\left[\begin{array}{ccc}1& 1& 3\\ {}1& 1& 3\\ {}1/3& 1/3& 1\end{array}\right] $$
(26)
$$ {A}^{C_{o-f}^T}=\left[\begin{array}{ccc}1& 1& 2\\ {}1& 1& 2\\ {}1/2& 1/2& 1\end{array}\right] $$
(27)
$$ {A}^{C_{WPD-t}^T}=\left[\begin{array}{ccc}1& 1& 4\\ {}1& 1& 4\\ {}1/4& 1/4& 1\end{array}\right] $$
(28)
$$ {A}^{C_{WPD-f}^T}=\left[\begin{array}{ccc}1& 1& 4\\ {}1& 1& 4\\ {}1/4& 1/4& 1\end{array}\right] $$
(29)
$$ {A}^{C_{EEMD-t}^T}=\left[\begin{array}{ccc}1& 1& 3\\ {}1& 1& 3\\ {}1/3& 1/3& 1\end{array}\right] $$
(30)
$$ {A}^{C_{EEMD-f}^T}=\left[\begin{array}{ccc}1& 1& 4\\ {}1& 1& 4\\ {}1/4& 1/4& 1\end{array}\right] $$
(31)

The constructed pairwise comparison matrix should be subject to some inconsistency due to some possible intransitivity in those comparisons. Saaty [43] proposes that the inconsistency be measured by a consistency index (CI) defined as

$$ CI=\frac{\lambda_{\mathrm{max}}-n}{n-1} $$
(32)

where λmax is the maximum eigenvalue of the comparison matrix and n is the number of indicators in the matrix. The interpretation of CI depends on the size of the matrix and requires to divide CI by the average consistency index of a matrix of randomly generated comparisons. This average value is termed as a random consistency index (RI), and the ratio between CI and RI is termed consistency ratio (CR), and can be interpreted as the percentage of inconsistency in the pairwise comparison matrix. The values of RI for different numbers of indicators are shown in Table 10.

Table 10 Values of the random consistency index (RI) for different numbers of indicators
Full size table

According to Table 10, the calculation of CR is not required for the matrices with 2 or fewer indicators, such as ACand \( {A}^{C^H} \). The values of CR for \( {A}^{C_p^H} \) and \( {A}^{C^T} \) are 0.038, respectively, and for other matrices are 0. Since the values of CR for all the matrices are less than 0.1, their inconsistency is acceptable for the further computation.

After the measuring of CR, the weight of the pairwise comparison matrix for hardware and time costs in AC is

$$ {w}_C={\left[0.833\kern0.5em 0.167\right]}^T $$
(33)

The weights of the pairwise comparison matrices for hardware cost can be computed from \( {A}^{C^H} \), \( {A}^{C_p^H} \), and \( {A}^{C_i^H} \):

$$ {w}_{C^H}={\left[0.75\kern0.5em 0.25\right]}^T $$
(34)
$$ {w}_{C_p^H}={\left[0.057\kern0.5em 0.597\kern0.5em 0.346\right]}^T $$
(35)
$$ {w}_{C_i^H}={\left[0.091\kern0.5em 0.455\kern0.5em 0.455\right]}^T $$
(36)

The weights of dynamometer, accelerometer, and AE sensor with respect to the hardware cost can be calculated by

$$ {\displaystyle \begin{array}{c}{w}^H={w}_{C^H}\times {\left[{w}_{C_p^H}\kern0.5em {w}_{C_i^H}\right]}^T\\ {}\kern1.32em =\left[\begin{array}{cc}0.75& 0.25\end{array}\right]\times \left[\begin{array}{c}\begin{array}{ccc}0.057& 0.597& 0.346\end{array}\\ {}\begin{array}{ccc}0.091& 0.455& 0.455\end{array}\end{array}\right]\\ {}\kern1.32em =\left[\begin{array}{ccc}0.066& 0.562& 0.372\end{array}\right]\end{array}} $$
(37)

The weights of the pairwise comparison matrices for time cost can be computed as

$$ {w}_{C^T}={\left[0.355\kern0.5em 0.221\kern0.5em \begin{array}{cccc}0.221& 0.142& 0.036& 0.025\end{array}\right]}^T $$
(38)
$$ {w}_{C_{o-t}^T}={\left[0.429\kern0.5em 0.429\kern0.5em 0.142\right]}^T $$
(39)
$$ {w}_{C_{o-f}^T}={\left[0.4\kern0.5em 0.4\kern0.5em 0.2\right]}^T $$
(40)
$$ {w}_{C_{WPD-t}^T}={\left[0.445\kern0.5em 0.445\kern0.5em 0.110\right]}^T $$
(41)
$$ {w}_{C_{WPD-f}^T}={\left[0.445\kern0.5em 0.445\kern0.5em 0.110\right]}^T $$
(42)
$$ {w}_{C_{EEMD-t}^T}={\left[0.429\kern0.5em 0.429\kern0.5em 0.142\right]}^T $$
(43)
$$ {w}_{C_{EEMD-f}^T}={\left[0.445\kern0.5em 0.445\kern0.5em 0.110\right]}^T $$
(44)

The weights of dynamometer, accelerometer, and AE sensor with respect to the hardware cost can be calculated by

$$ {\displaystyle \begin{array}{c}{w}^T={w}_{C^T}\times {\left[{w}_{C_{o-t}^T}\kern0.5em {w}_{C_{o-f}^T}\kern0.5em {w}_{C_{WPD-t}^T}\kern0.5em {w}_{C_{WPD-f}^T}\kern0.5em {w}_{C_{EEMD-t}^T}\kern0.5em {w}_{C_{EEMD-f}^T}\right]}^T\\ {}\kern1.32em =\left[\begin{array}{cccccc}0.355& 0.221& 0.221& 0.142& 0.036& 0.025\end{array}\right]\times \left[\begin{array}{ccc}0.429& 0.429& 0.142\\ {}0.4& 0.4& 0.2\\ {}0.445& 0.445& 0.110\\ {}0.445& 0.445& 0.110\\ {}0.429& 0.429& 0.142\\ {}0.445& 0.445& 0.110\end{array}\right]\\ {}\kern1.32em =\left[\begin{array}{ccc}0.429& 0.429& 0.142\end{array}\right]\end{array}} $$
(45)

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Guo, W., Wu, C., Ding, Z. et al. Prediction of surface roughness based on a hybrid feature selection method and long short-term memory network in grinding. Int J Adv Manuf Technol 112, 2853–2871 (2021). https://doi.org/10.1007/s00170-020-06523-z

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