1 Introduction
2 Materials and methods
2.1 Workpiece setup and cutting parameters
S. no | D.O.C (mm) | Feed (mm/rev) | Cutting speed (m/min) | Material |
---|---|---|---|---|
1 | 1.5 | 0.5 | 200 | Cast iron |
2 | 0.75 | 0.5 | 200 | Cast iron |
3 | 0.75 | 0.25 | 200 | Cast iron |
4 | 1.5 | 0.25 | 200 | Cast iron |
5 | 1.5 | 0.5 | 200 | Cast iron |
6 | 1.5 | 0.25 | 200 | Cast iron |
7 | 0.75 | 0.25 | 200 | Cast iron |
8 | 0.75 | 0.5 | 200 | Cast iron |
9 | 1.5 | 0.5 | 200 | Steel |
10 | 1.5 | 0.25 | 200 | Steel |
11 | 0.75 | 0.25 | 200 | Steel |
12 | 0.75 | 0.5 | 200 | Steel |
13 | 0.75 | 0.25 | 200 | Steel |
14 | 0.75 | 0.5 | 200 | Steel |
15 | 1.5 | 0.25 | 200 | Steel |
16 | 1.5 | 0.5 | 200 | Steel |
2.2 Vibration and acoustic signals
2.3 Selection of mother wavelet
2.4 SinGAN
2.5 Long short-term memory network
3 Results and discussion
Wavelet | Maximum relative wavelet energy for spindle acoustic emission | Maximum relative wavelet energy for spindle vibration |
---|---|---|
Coiflet1 | 0.018 | 0.017 |
Daubechies1 | 0.019 | 0.016 |
Meyr | 0.019 | 0.017 |
Morlet | 0.021 | 0.018 |
Reverse biorthogonal1.1 | 0.019 | 0.017 |
Symlet | 0.018 | 0.017 |
Sr. no | IQP features |
---|---|
1 | Structural Similarity Index Measure (SSIM) |
2 | Chromaticity similarity value (CS value) |
3 | Mean square error (MSE) |
4 | Multiscale Structural Similarity Index Measure (MSSIM) |
5 | Root mean squared error (RMSE) |
6 | Root mean squared error using sliding window (RMSESW) |
7 | Relative average spectral error (RASE) |
8 | Erreur Relative Globale Adimensionnelle de Synthèse (ERGAS) |
9 | Peak signal to noise ratio (PSNR) |
10 | Universal Quality Image Index (UQI) |
11 | Spatial correlation coefficient (SCC) |
12 | Spectral angle mapper (SAM) |
13 | Visual information fidelity (VIF) |
14 | Block sensitive—peak signal-to-noise ratio (PSNRB) |
Sr. no | SSIM | CS value | MSE | MSSIM | RMSE | RMSESW | RASE | ERGAS | PSNR | UQI | SSC | SAM | VIFP | PSNRB |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0.8952 | 0.9259 | 312.3712 | 0.9715 | 17.6740 | 17.4194 | 1479.834 | 5919.335 | 23.1841 | 0.9343 | 0.0427 | 0.0756 | 0.0903 | 23.1841 |
2 | 0.8967 | 0.9276 | 312.9153 | 0.9713 | 17.6894 | 17.4467 | 1482.276 | 5929.107 | 23.1765 | 0.9341 | 0.0534 | 0.0752 | 0.1063 | 23.1765 |
3 | 0.8947 | 0.9250 | 308.4781 | 0.9709 | 17.5635 | 17.3234 | 1471.954 | 5887.819 | 23.2386 | 0.9351 | 0.0572 | 0.0754 | 0.1054 | 23.2386 |
4 | 0.8904 | 0.9209 | 311.5191 | 0.9671 | 17.6499 | 17.4131 | 1479.060 | 5916.242 | 23.1960 | 0.9343 | 0.0350 | 0.0774 | 0.0973 | 23.1960 |
5 | 0.8920 | 0.9224 | 309.6551 | 0.9691 | 17.5970 | 17.3688 | 1475.559 | 5902.239 | 23.2220 | 0.9348 | 0.0329 | 0.0758 | 0.0970 | 23.2220 |
6 | 0.8909 | 0.9213 | 309.3633 | 0.9689 | 17.5887 | 17.3663 | 1475.201 | 5900.804 | 23.2261 | 0.9346 | 0.0277 | 0.0800 | 0.0872 | 23.2261 |
7 | 0.8926 | 0.9231 | 312.7855 | 0.9710 | 17.6857 | 17.4011 | 1478.024 | 5912.097 | 23.1783 | 0.9345 | 0.0419 | 0.0765 | 0.0941 | 23.1783 |
8 | 0.8934 | 0.9242 | 311.6493 | 0.9674 | 17.6536 | 17.4554 | 1482.745 | 5930.981 | 23.1941 | 0.9340 | 0.0412 | 0.0773 | 0.0907 | 23.1941 |
9 | 0.8929 | 0.9235 | 311.6109 | 0.9685 | 17.6525 | 17.4300 | 1480.620 | 5922.483 | 23.1947 | 0.9341 | 0.0374 | 0.0774 | 0.0951 | 23.1947 |
10 | 0.8907 | 0.9206 | 307.7825 | 0.9674 | 17.5437 | 17.2556 | 1465.860 | 5863.441 | 23.2484 | 0.9356 | 0.0381 | 0.0775 | 0.0936 | 23.2484 |
11 | 0.8931 | 0.9235 | 309.5145 | 0.9689 | 17.5930 | 17.3629 | 1474.839 | 5899.358 | 23.2240 | 0.9347 | 0.0523 | 0.0771 | 0.1004 | 23.2240 |
12 | 0.8944 | 0.9244 | 307.0365 | 0.9681 | 17.5225 | 17.2513 | 1465.449 | 5861.798 | 23.2589 | 0.9356 | 0.0460 | 0.0758 | 0.1035 | 23.2589 |
13 | 0.8929 | 0.9230 | 306.6827 | 0.9692 | 17.5124 | 17.2786 | 1467.945 | 5871.783 | 23.2639 | 0.9354 | 0.0356 | 0.0770 | 0.0975 | 23.2639 |
14 | 0.8893 | 0.9197 | 311.9580 | 0.9656 | 17.6623 | 17.3947 | 1477.243 | 5908.971 | 23.1898 | 0.9344 | 0.0330 | 0.0788 | 0.0830 | 23.1898 |
15 | 0.8937 | 0.9239 | 308.3911 | 0.9683 | 17.5611 | 17.2998 | 1469.816 | 5879.266 | 23.2398 | 0.9353 | 0.0430 | 0.0759 | 0.0968 | 23.2398 |
Sr. no | SSIM | CS value | MSE | MSSIM | RMSE | RMSESW | RASE | ERGAS | PSNR | UQI | SSC | SAM | VIFP | PSNRB |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0.9547 | 0.9879 | 300.0067 | 0.9927 | 17.3207 | 17.2208 | 1483.103 | 5932.4142 | 23.3595 | 0.9338 | 0.0333 | 0.0749 | 0.3268 | 23.3595 |
2 | 0.9552 | 0.9888 | 301.6342 | 0.9927 | 17.3676 | 17.3051 | 1490.434 | 5961.7371 | 23.3360 | 0.9331 | 0.0426 | 0.0763 | 0.3191 | 23.3360 |
3 | 0.9549 | 0.9884 | 299.8952 | 0.9924 | 17.3175 | 17.2618 | 1486.792 | 5947.1701 | 23.3611 | 0.9334 | 0.0440 | 0.0810 | 0.3500 | 23.3611 |
4 | 0.9544 | 0.9877 | 300.9377 | 0.9922 | 17.3476 | 17.2390 | 1484.730 | 5938.9206 | 23.3460 | 0.9337 | 0.0383 | 0.0917 | 0.3876 | 23.3460 |
5 | 0.9547 | 0.9883 | 301.3370 | 0.9926 | 17.3591 | 17.2833 | 1488.575 | 5954.3020 | 23.3403 | 0.9333 | 0.0445 | 0.0861 | 0.3586 | 23.3403 |
6 | 0.9542 | 0.9876 | 300.8992 | 0.9918 | 17.3464 | 17.2551 | 1486.116 | 5944.4658 | 23.3466 | 0.9335 | 0.0410 | 0.0889 | 0.3605 | 23.3466 |
7 | 0.9555 | 0.9890 | 300.9690 | 0.9930 | 17.3485 | 17.2668 | 1487.182 | 5948.7294 | 23.3456 | 0.9334 | 0.0429 | 0.0796 | 0.3420 | 23.3456 |
8 | 0.9546 | 0.9882 | 301.6104 | 0.9923 | 17.3669 | 17.2886 | 1488.998 | 5955.9932 | 23.3363 | 0.9332 | 0.0392 | 0.0865 | 0.3590 | 23.3363 |
9 | 0.9549 | 0.9882 | 300.3795 | 0.9925 | 17.3315 | 17.2288 | 1483.896 | 5935.5844 | 23.3541 | 0.9338 | 0.0397 | 0.0902 | 0.3863 | 23.3541 |
10 | 0.9552 | 0.9885 | 299.1172 | 0.9927 | 17.2950 | 17.2241 | 1483.558 | 5934.2355 | 23.3724 | 0.9338 | 0.0446 | 0.0822 | 0.3746 | 23.3724 |
11 | 0.9550 | 0.9881 | 298.1654 | 0.9925 | 17.2675 | 17.1917 | 1480.791 | 5923.1644 | 23.3862 | 0.9340 | 0.0436 | 0.0852 | 0.3666 | 23.3862 |
12 | 0.9552 | 0.9886 | 300.0177 | 0.9926 | 17.3210 | 17.2564 | 1486.312 | 5945.2495 | 23.3593 | 0.9335 | 0.0345 | 0.0761 | 0.3328 | 23.3593 |
13 | 0.9546 | 0.9881 | 300.9883 | 0.9923 | 17.3490 | 17.2745 | 1487.842 | 5951.3705 | 23.3453 | 0.9333 | 0.0441 | 0.0850 | 0.3590 | 23.3453 |
14 | 0.9549 | 0.9883 | 299.9030 | 0.9925 | 17.3177 | 17.2450 | 1485.333 | 5941.3322 | 23.3610 | 0.9336 | 0.0412 | 0.0823 | 0.3574 | 23.3610 |
15 | 0.9549 | 0.9883 | 301.2826 | 0.9925 | 17.3575 | 17.2536 | 1485.999 | 5943.9980 | 23.3411 | 0.9335 | 0.0400 | 0.0862 | 0.3545 | 23.3411 |
Sr. no | SSIM | CS value | MSE | MSSIM | RMSE | RMSESW | RASE | ERGAS | PSNR | UQI | SSC | SAM | VIFP | PSNRB |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | −1.01998 | −0.98427 | 0.119164 | −1.54133 | 0.119951 | 0.197731 | 0.339522 | 0.339522 | −0.12072 | −0.33401 | −1.01482 | 0.391285 | −1.42399 | −0.1208 |
2 | −0.96556 | −0.9277 | 0.137216 | −1.56052 | 0.138062 | 0.245591 | 0.398751 | 0.398751 | −0.13889 | −0.3898 | −0.88398 | 0.380023 | −1.31061 | −0.13898 |
3 | −1.03738 | −1.01322 | −0.01001 | −1.6104 | −0.01011 | 0.029294 | 0.148483 | 0.148483 | 0.010203 | −0.12706 | −0.83716 | 0.38775 | −1.31699 | 0.010224 |
4 | −1.18769 | −1.14939 | 0.090893 | −2.06087 | 0.091556 | 0.186572 | 0.32077 | 0.32077 | −0.09221 | −0.337 | −1.10854 | 0.442139 | −1.37404 | −0.09226 |
5 | −1.13064 | −1.10029 | 0.029045 | −1.81915 | 0.029301 | 0.108829 | 0.235891 | 0.235891 | −0.02955 | −0.21238 | −1.13422 | 0.398879 | −1.37665 | −0.02956 |
6 | −1.17122 | −1.13661 | 0.019364 | −1.84824 | 0.019539 | 0.10447 | 0.227189 | 0.227189 | −0.01971 | −0.26018 | −1.19845 | 0.512789 | −1.44595 | −0.01971 |
7 | −1.11138 | −1.07628 | 0.13291 | −1.58981 | 0.133743 | 0.165478 | 0.295644 | 0.295644 | −0.13456 | −0.28934 | −1.02487 | 0.415819 | −1.39695 | −0.13464 |
8 | −1.0822 | −1.04083 | 0.095211 | −2.03299 | 0.095895 | 0.260778 | 0.410113 | 0.410113 | −0.09657 | −0.41731 | −1.03325 | 0.439216 | −1.42079 | −0.09663 |
9 | −1.10085 | −1.06158 | 0.093936 | −1.89352 | 0.094615 | 0.216234 | 0.358603 | 0.358603 | −0.09528 | −0.37979 | −1.07941 | 0.44085 | −1.38967 | −0.09534 |
10 | −1.17786 | −1.15976 | −0.03309 | −2.034 | −0.03343 | −0.08967 | 0.000709 | 0.000709 | 0.03377 | 0.004422 | −1.07019 | 0.44554 | −1.40026 | 0.033808 |
11 | −1.09213 | −1.0628 | 0.024378 | −1.84439 | 0.024595 | 0.098567 | 0.218425 | 0.218425 | −0.02481 | −0.22581 | −0.8976 | 0.4324 | −1.35234 | −0.02482 |
12 | −1.04645 | −1.03222 | −0.05784 | −1.94873 | −0.05847 | −0.09709 | −0.00925 | −0.00925 | 0.059104 | 0.008417 | −0.97397 | 0.397429 | −1.3305 | 0.05916 |
13 | −1.09936 | −1.07933 | −0.06958 | −1.81253 | −0.07036 | −0.04934 | 0.051276 | 0.051276 | 0.071138 | −0.05625 | −1.1008 | 0.431709 | −1.37307 | 0.071204 |
14 | −1.22676 | −1.18956 | 0.105454 | −2.24818 | 0.106186 | 0.154264 | 0.276699 | 0.276699 | −0.1069 | −0.31154 | −1.13375 | 0.480522 | −1.47554 | −0.10697 |
15 | −1.07098 | −1.04867 | −0.0129 | −1.91907 | −0.01302 | −0.01213 | 0.096638 | 0.096638 | 0.013149 | −0.07771 | −1.01048 | 0.401078 | −1.37798 | 0.013172 |
Sr. no | SSIM | CS value | MSE | MSSIM | RMSE | RMSESW | RASE | ERGAS | PSNR | UQI | SSC | SAM | VIFP | PSNRB |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0.273811 | 0.39698 | −0.22674 | 0.325791 | −0.22893 | −0.07278 | 0.2232 | 0.2232 | 0.231135 | −0.23977 | −1.01943 | 0.355105 | −0.52731 | 0.231135 |
2 | 0.312827 | 0.475412 | −0.13009 | 0.317693 | −0.13117 | 0.304602 | 0.569219 | 0.569219 | 0.132251 | −0.56574 | −0.81951 | 0.390622 | −0.57759 | 0.132251 |
3 | 0.292096 | 0.43559 | −0.23336 | 0.255493 | −0.23564 | 0.110897 | 0.397324 | 0.397324 | 0.237926 | −0.40211 | −0.78966 | 0.504637 | −0.37615 | 0.237926 |
4 | 0.247217 | 0.37325 | −0.17145 | 0.191521 | −0.17298 | 0.008674 | 0.299978 | 0.299978 | 0.174507 | −0.28521 | −0.91309 | 0.76385 | −0.13089 | 0.174507 |
5 | 0.27661 | 0.425137 | −0.14774 | 0.299173 | −0.14901 | 0.207074 | 0.481483 | 0.481483 | 0.150272 | −0.46683 | −0.77934 | 0.628666 | −0.32039 | 0.150272 |
6 | 0.230224 | 0.363322 | −0.17374 | 0.088921 | −0.17529 | 0.080545 | 0.365413 | 0.365413 | 0.176843 | −0.35893 | −0.85396 | 0.695514 | −0.30745 | 0.176843 |
7 | 0.338991 | 0.488245 | −0.1696 | 0.412295 | −0.1711 | 0.132891 | 0.415724 | 0.415724 | 0.172605 | −0.41794 | −0.815 | 0.470846 | −0.42836 | 0.172605 |
8 | 0.266043 | 0.415964 | −0.1315 | 0.209022 | −0.1326 | 0.230586 | 0.501439 | 0.501439 | 0.133693 | −0.48521 | −0.89237 | 0.637941 | −0.3176 | 0.133693 |
9 | 0.289822 | 0.41685 | −0.2046 | 0.278051 | −0.20652 | −0.03728 | 0.26061 | 0.26061 | 0.208437 | −0.25795 | −0.8836 | 0.728563 | −0.1396 | 0.208437 |
10 | 0.317315 | 0.446811 | −0.27956 | 0.313235 | −0.28247 | −0.05819 | 0.244693 | 0.244693 | 0.285399 | −0.25794 | −0.77722 | 0.5324 | −0.2159 | 0.285399 |
11 | 0.295575 | 0.409603 | −0.33608 | 0.279571 | −0.33985 | −0.20317 | 0.11405 | 0.11405 | 0.343647 | −0.13136 | −0.79791 | 0.605941 | −0.26816 | 0.343647 |
12 | 0.312927 | 0.456093 | −0.22609 | 0.304693 | −0.22827 | 0.086542 | 0.37466 | 0.37466 | 0.230464 | −0.38647 | −0.99332 | 0.384135 | −0.48789 | 0.230464 |
13 | 0.263858 | 0.40836 | −0.16845 | 0.227926 | −0.16994 | 0.167554 | 0.44689 | 0.44689 | 0.171433 | −0.4367 | −0.78802 | 0.601263 | −0.31778 | 0.171433 |
14 | 0.293533 | 0.429766 | −0.2329 | 0.271857 | −0.23517 | 0.035567 | 0.328436 | 0.328436 | 0.237453 | −0.33484 | −0.85074 | 0.537087 | −0.3282 | 0.237453 |
15 | 0.290108 | 0.427016 | −0.15097 | 0.269882 | −0.15227 | 0.073761 | 0.359893 | 0.359893 | 0.153568 | −0.34934 | −0.87565 | 0.630472 | −0.34695 | 0.153568 |
Performance metric | Formulas | Ideal value |
---|---|---|
R2 | \(1-\frac{\sum_{{\varvec{i}}}{({{\varvec{y}}}_{{\varvec{p}}}-{{\varvec{y}}}_{{\varvec{r}}})}^{2}}{{\sum }_{{\varvec{i}}}{({{\varvec{y}}}_{{\varvec{p}}}-\overline{{\varvec{y}} })}^{2}}\) | ˜1 |
Adjusted R2 | \(1- \left[\frac{(N-1)(1-{R}^{2})}{(N-v-1)}\right]\) | ˜1 |
Mean absolute error (MAE) | \(MAE= \frac{1}{N}\sum\limits_{i=1}^{N}\left|{y}_{p}-{y}_{r}\right|\) | ˜0 |
Root mean square error (RMSE) | \(RMSE=\sqrt{\frac{1}{{\varvec{N}}}\sum\limits_{{\varvec{i}}=1}^{{\varvec{N}}}{{\varvec{y}}}_{{\varvec{r}}}-{{\varvec{y}}}_{{\varvec{p}}}}\) | ˜0 |
Mean square error (MSE) | \(MSE= \frac{1}{N}\sum\limits_{i=1}^{N}{y}_{r}-{y}_{p}\) | ˜0 |
References | Material of workpiece | Sensors used | Algorithm | RMSE | MAE | R2 |
---|---|---|---|---|---|---|
Hanachi et. al [45] | Cast iron | Current sensors | Sipos | 0.42 | - | 0.429 |
Adaptive neuro-fuzzy inference system (ANFIS) | 0.56 | - | 0.289 | |||
Regularized particle filter (RPF) | 0.22 | - | 0.086 | |||
Yuan et al. [46] | Cast iron and steel | All sensors are considered | CNN | 0.0836 | 0.0671 | 0.8725 |
Traini et al. [47] | Cast iron and steel | All sensors are considered | Logistic regression | 0.11 | - | 0.817 |
Decision forest | 0.123 | - | 0.781 | |||
Decision jungle | 0.116 | - | 0.813 | |||
Boosted decision tree | 0.122 | - | 0.794 | |||
Neural network | 0.11 | - | 0.821 | |||
Cai et al. [48] | Cast iron and steel | All sensors are considered | Temporal encoder deep LSTM | 0.0456 | 0.0322 | 0.90 |
Kumar et al. [49] | Cast iron and steel | Vibration | Vanilla LSTM | 0.1129 | 0.091 | 0.773 |
Bidirectional LSTM | 0.0982 | 0.0764 | 0.8366 | |||
Encoder—decoder LSTM | 0.0586 | 0.0431 | 0.9489 | |||
Hybrid LSTM | 0.0364 | 0.0258 | 0.9837 | |||
Zhou and Sun [50] | Cast iron and steel | Current sensors | Kernel extreme learning machine (KELM) | 0.013 | 0.0926 | - |
Two-layer angle KELM (TAKELM) | 0.003 | 0.0134 | - | |||
Least squares SVM (LS-SVM) | 0.012 | 0.0254 | - | |||
Proposed work | Steel | AE and vibration sensors | Vanilla LSTM | 0.0472 | 0.0284 | 0.9822 |
Bidirectional LSTM | 0.0663 | 0.0393 | 0.9649 | |||
Stacked LSTM | 0.0233 | 0.0090 | 0.9957 |
4 Conclusion
-
Tool wear prediction was found to be extremely well from both AE and vibration feature vectors.
-
The lowest MAE, RMSE, and MSE values (testing) observed from AE feature vector are 0.008, 0.023, and 0.0005, respectively, whereas from vibration signals 0.005, 0.016, and 0.0002 values (testing) are observed.
-
Significantly high R2 and Adj. R2 values of 0.997 are observed from the vibration feature vector as compared to 0.995 with the AE feature vector.
-
Stacked LSTM predicted tool wear much better as compared to bidirectional LSTM and vanilla LSTM models in case of AE and vibration feature vectors both.
-
Superior prediction of tool wear is achieved with the proposed methodology, specifically when the availability of experimental data set is less to train the model.