Modified DEMATEL Method Based on Objective Data Grey Relational Analysis for Time Series
Abstract
:1. Introduction
2. Method
2.1. Evaluate Correlation between Categories Using Grey Relational Analysis
- (i)
- Obtain the initial image of each sequence:
- (ii)
- Find the absolute value sequence of the difference between the corresponding components of the initial image of and , denoted by , where
- (iii)
- Find the maximum and minimum of , , :
- (iv)
- Compute the k-point relation coefficient:
- (v)
- Find the GRD:
2.2. Determine Priority of Categories Using Modified DEMATEL
- (i)
- Obtain the direct relation matrix by GRD between sequences and (). Specifically, the direct relation matrix satisfies
- (ii)
- Find the normalized direct relation matrix :
- (iii)
- Obtain the total relation matrix , which satisfies:
- (iv)
- Obtain the prominence and relation:
3. Experiment
3.1. Simulation Experiment
3.2. Case Study
3.2.1. Evaluate Correlation between Data Categories Using GRA
3.2.2. Determine Priority of Data Categories Using Modified DEMATEL
3.2.3. Results of Remaining Useful Life Prediction
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
ES1 | ES2 | ES3 | ES4 | ES5 | ES6 | ES7 | ES8 | ES9 | ES10 | ES11 | ES12 | ES13 | ES14 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ES1 | 0.0000 | 0.8377 | 0.7334 | 0.8200 | 0.9115 | 0.9015 | 0.7893 | 0.8721 | 0.9125 | 0.8904 | 0.8210 | 0.8286 | 0.6679 | 0.6877 |
ES2 | 0.8761 | 0.0000 | 0.7780 | 0.8307 | 0.8696 | 0.8586 | 0.8607 | 0.8407 | 0.8697 | 0.8651 | 0.8584 | 0.8530 | 0.7377 | 0.7471 |
ES3 | 0.8280 | 0.8207 | 0.0000 | 0.7711 | 0.8057 | 0.8320 | 0.8474 | 0.7890 | 0.8060 | 0.8119 | 0.8625 | 0.8629 | 0.7001 | 0.7090 |
ES4 | 0.8542 | 0.8217 | 0.7107 | 0.0000 | 0.9044 | 0.8322 | 0.7745 | 0.9284 | 0.9039 | 0.8857 | 0.7830 | 0.7825 | 0.8018 | 0.8204 |
ES5 | 0.9177 | 0.8402 | 0.7187 | 0.8879 | 0.0000 | 0.8815 | 0.7872 | 0.9279 | 0.9986 | 0.9166 | 0.8054 | 0.8143 | 0.7193 | 0.7390 |
ES6 | 0.9284 | 0.8630 | 0.7978 | 0.8458 | 0.9071 | 0.0000 | 0.8306 | 0.8906 | 0.9076 | 0.9304 | 0.8594 | 0.8708 | 0.7244 | 0.7421 |
ES7 | 0.8490 | 0.8721 | 0.8237 | 0.8007 | 0.8371 | 0.8391 | 0.0000 | 0.8097 | 0.8371 | 0.8354 | 0.8828 | 0.8692 | 0.7255 | 0.7325 |
ES8 | 0.8945 | 0.8275 | 0.7256 | 0.9261 | 0.9371 | 0.8774 | 0.7788 | 0.0000 | 0.9369 | 0.9137 | 0.7972 | 0.8026 | 0.7586 | 0.7798 |
ES9 | 0.9186 | 0.8402 | 0.7189 | 0.8872 | 0.9986 | 0.8821 | 0.7872 | 0.9277 | 0.0000 | 0.9167 | 0.8056 | 0.8146 | 0.7188 | 0.7385 |
ES10 | 0.9150 | 0.8610 | 0.7629 | 0.8885 | 0.9307 | 0.9254 | 0.8165 | 0.9183 | 0.9308 | 0.0000 | 0.8371 | 0.8438 | 0.7472 | 0.7654 |
ES11 | 0.8695 | 0.8659 | 0.8361 | 0.8031 | 0.8475 | 0.8626 | 0.8791 | 0.8211 | 0.8477 | 0.8499 | 0.0000 | 0.8863 | 0.7122 | 0.7230 |
ES12 | 0.8684 | 0.8530 | 0.8279 | 0.7928 | 0.8465 | 0.8666 | 0.8574 | 0.8170 | 0.8468 | 0.8482 | 0.8797 | 0.0000 | 0.6941 | 0.7069 |
ES13 | 0.7808 | 0.7842 | 0.7001 | 0.8497 | 0.8086 | 0.7678 | 0.7563 | 0.8197 | 0.8082 | 0.7990 | 0.7505 | 0.7459 | 0.0000 | 0.9003 |
ES14 | 0.7877 | 0.7848 | 0.6997 | 0.8587 | 0.8163 | 0.7752 | 0.7546 | 0.8297 | 0.8160 | 0.8070 | 0.7520 | 0.7487 | 0.8959 | 0.0000 |
ES1 | ES2 | ES3 | ES4 | ES5 | ES6 | ES7 | ES8 | ES9 | ES10 | ES11 | ES12 | ES13 | ES14 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ES1 | 0.0000 | 0.0733 | 0.0642 | 0.0718 | 0.0798 | 0.0789 | 0.0691 | 0.0764 | 0.0799 | 0.0780 | 0.0719 | 0.0725 | 0.0585 | 0.0602 |
ES2 | 0.0767 | 0.0000 | 0.0681 | 0.0727 | 0.0761 | 0.0752 | 0.0754 | 0.0736 | 0.0761 | 0.0757 | 0.0752 | 0.0747 | 0.0646 | 0.0654 |
ES3 | 0.0725 | 0.0719 | 0.0000 | 0.0675 | 0.0705 | 0.0728 | 0.0742 | 0.0691 | 0.0706 | 0.0711 | 0.0755 | 0.0755 | 0.0613 | 0.0621 |
ES4 | 0.0748 | 0.0719 | 0.0622 | 0.0000 | 0.0792 | 0.0729 | 0.0678 | 0.0813 | 0.0791 | 0.0775 | 0.0686 | 0.0685 | 0.0702 | 0.0718 |
ES5 | 0.0803 | 0.0736 | 0.0629 | 0.0777 | 0.0000 | 0.0772 | 0.0689 | 0.0812 | 0.0874 | 0.0803 | 0.0705 | 0.0713 | 0.0630 | 0.0647 |
ES6 | 0.0813 | 0.0756 | 0.0698 | 0.0740 | 0.0794 | 0.0000 | 0.0727 | 0.0780 | 0.0795 | 0.0815 | 0.0752 | 0.0762 | 0.0634 | 0.0650 |
ES7 | 0.0743 | 0.0764 | 0.0721 | 0.0701 | 0.0733 | 0.0735 | 0.0000 | 0.0709 | 0.0733 | 0.0731 | 0.0773 | 0.0761 | 0.0635 | 0.0641 |
ES8 | 0.0783 | 0.0725 | 0.0635 | 0.0811 | 0.0820 | 0.0768 | 0.0682 | 0.0000 | 0.0820 | 0.0800 | 0.0698 | 0.0703 | 0.0664 | 0.0683 |
ES9 | 0.0804 | 0.0736 | 0.0629 | 0.0777 | 0.0874 | 0.0772 | 0.0689 | 0.0812 | 0.0000 | 0.0803 | 0.0705 | 0.0713 | 0.0629 | 0.0647 |
ES10 | 0.0801 | 0.0754 | 0.0668 | 0.0778 | 0.0815 | 0.0810 | 0.0715 | 0.0804 | 0.0815 | 0.0000 | 0.0733 | 0.0739 | 0.0654 | 0.0670 |
ES11 | 0.0761 | 0.0758 | 0.0732 | 0.0703 | 0.0742 | 0.0755 | 0.0770 | 0.0719 | 0.0742 | 0.0744 | 0.0000 | 0.0776 | 0.0624 | 0.0633 |
ES12 | 0.0760 | 0.0747 | 0.0725 | 0.0694 | 0.0741 | 0.0759 | 0.0751 | 0.0715 | 0.0741 | 0.0743 | 0.0770 | 0.0000 | 0.0608 | 0.0619 |
ES13 | 0.0684 | 0.0687 | 0.0613 | 0.0744 | 0.0708 | 0.0672 | 0.0662 | 0.0718 | 0.0708 | 0.0700 | 0.0657 | 0.0653 | 0.0000 | 0.0788 |
ES14 | 0.0690 | 0.0687 | 0.0613 | 0.0752 | 0.0715 | 0.0679 | 0.0661 | 0.0726 | 0.0714 | 0.0707 | 0.0658 | 0.0655 | 0.0784 | 0.0000 |
ES1 | ES2 | ES3 | ES4 | ES5 | ES6 | ES7 | ES8 | ES9 | ES10 | ES11 | ES12 | ES13 | ES14 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ES1 | 1.1725 | 1.1989 | 1.0888 | 1.2065 | 1.2596 | 1.2274 | 1.1601 | 1.2339 | 1.2598 | 1.2429 | 1.1799 | 1.1836 | 1.0595 | 1.0796 |
ES2 | 1.2601 | 1.1464 | 1.1067 | 1.2232 | 1.2729 | 1.2403 | 1.1809 | 1.2477 | 1.2730 | 1.2573 | 1.1984 | 1.2011 | 1.0790 | 1.0985 |
ES3 | 1.2153 | 1.1738 | 1.0069 | 1.1786 | 1.2264 | 1.1977 | 1.1415 | 1.2028 | 1.2265 | 1.2121 | 1.1597 | 1.1627 | 1.0408 | 1.0596 |
ES4 | 1.2540 | 1.2092 | 1.0975 | 1.1513 | 1.2712 | 1.2339 | 1.1701 | 1.2501 | 1.2713 | 1.2546 | 1.1884 | 1.1914 | 1.0803 | 1.1005 |
ES5 | 1.2753 | 1.2264 | 1.1125 | 1.2393 | 1.2145 | 1.2538 | 1.1864 | 1.2663 | 1.2950 | 1.2733 | 1.2056 | 1.2095 | 1.0878 | 1.1083 |
ES6 | 1.2902 | 1.2418 | 1.1311 | 1.2498 | 1.3023 | 1.1961 | 1.2030 | 1.2774 | 1.3024 | 1.2884 | 1.2233 | 1.2273 | 1.1003 | 1.1209 |
ES7 | 1.2443 | 1.2041 | 1.0982 | 1.2075 | 1.2565 | 1.2253 | 1.0980 | 1.2316 | 1.2566 | 1.2413 | 1.1873 | 1.1893 | 1.0662 | 1.0854 |
ES8 | 1.2732 | 1.2252 | 1.1128 | 1.2419 | 1.2900 | 1.2532 | 1.1854 | 1.1909 | 1.2901 | 1.2727 | 1.2047 | 1.2083 | 1.0907 | 1.1113 |
ES9 | 1.2754 | 1.2264 | 1.1126 | 1.2393 | 1.2949 | 1.2539 | 1.1864 | 1.2663 | 1.2146 | 1.2733 | 1.2057 | 1.2095 | 1.0878 | 1.1083 |
ES10 | 1.2938 | 1.2461 | 1.1324 | 1.2575 | 1.3087 | 1.2756 | 1.2062 | 1.2841 | 1.3088 | 1.2177 | 1.2259 | 1.2296 | 1.1060 | 1.1267 |
ES11 | 1.2552 | 1.2127 | 1.1074 | 1.2168 | 1.2668 | 1.2363 | 1.1783 | 1.2418 | 1.2669 | 1.2518 | 1.1245 | 1.1995 | 1.0732 | 1.0928 |
ES12 | 1.2453 | 1.2022 | 1.0981 | 1.2064 | 1.2567 | 1.2269 | 1.1674 | 1.2317 | 1.2569 | 1.2418 | 1.1866 | 1.1181 | 1.0634 | 1.0829 |
ES13 | 1.1926 | 1.1526 | 1.0478 | 1.1664 | 1.2075 | 1.1741 | 1.1167 | 1.1865 | 1.2076 | 1.1923 | 1.1330 | 1.1356 | 0.9672 | 1.0581 |
ES14 | 1.1989 | 1.1582 | 1.0528 | 1.1727 | 1.2139 | 1.1803 | 1.1219 | 1.1930 | 1.2139 | 1.1986 | 1.1385 | 1.1412 | 1.0448 | 0.9900 |
Appendix B
Engine Sensor | GRA-DEMATEL | Proposed Method | ||
---|---|---|---|---|
Ranking | Ranking | |||
ES1 | 22.4991 | 4 | 2.0338 | 6 |
ES2 | 20.9809 | 10 | 2.0139 | 8 |
ES3 | 21.3425 | 9 | 1.9068 | 12 |
ES4 | 22.5051 | 3 | 2.0176 | 7 |
ES5 | 18.7684 | 12 | 2.0642 | 3 |
ES6 | 11.6702 | 14 | 2.0507 | 4 |
ES7 | 22.1287 | 5 | 1.9774 | 11 |
ES8 | 22.5209 | 2 | 2.0468 | 5 |
ES9 | 18.7684 | 11 | 2.0643 | 2 |
ES10 | 12.1468 | 13 | 2.0664 | 1 |
ES11 | 22.0440 | 8 | 1.9974 | 9 |
ES12 | 22.6625 | 1 | 1.9926 | 10 |
ES13 | 22.1159 | 6 | 1.8749 | 14 |
ES14 | 22.0922 | 7 | 1.8931 | 13 |
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Factor | DEMATEL | Modified DEMATEL | ||
---|---|---|---|---|
Ranking | Ranking | |||
F1 | 1.9557 | 4 | 1.7415 | 4 |
F2 | 2.5704 | 3 | 2.2887 | 2 |
F3 | 1.6218 | 5 | 1.2752 | 5 |
F4 | 2.7364 | 1 | 2.2372 | 3 |
F5 | 2.7312 | 2 | 2.4574 | 1 |
Engine Sensor | ||||
---|---|---|---|---|
ES1 | 1.0395 | 0.9942 | 2.0338 | −0.0453 |
ES2 | 1.0079 | 1.0060 | 2.0139 | −0.0019 |
ES3 | 0.9306 | 0.9762 | 1.9068 | 0.0456 |
ES4 | 1.0147 | 1.0029 | 2.0176 | −0.0118 |
ES5 | 1.0496 | 1.0147 | 2.0642 | −0.0349 |
ES6 | 1.0259 | 1.0248 | 2.0507 | −0.0011 |
ES7 | 0.9814 | 0.9961 | 1.9774 | 0.0147 |
ES8 | 1.0324 | 1.0144 | 2.0468 | −0.0180 |
ES9 | 1.0496 | 1.0147 | 2.0643 | −0.0350 |
ES10 | 1.0383 | 1.0281 | 2.0664 | −0.0101 |
ES11 | 0.9946 | 1.0028 | 1.9974 | 0.0083 |
ES12 | 0.9968 | 0.9957 | 1.9926 | −0.0011 |
ES13 | 0.9123 | 0.9626 | 1.8749 | 0.0503 |
ES14 | 0.9264 | 0.9668 | 1.8931 | 0.0404 |
Rank of Proposed Method | Engine Sensor | Optimal RMSE | RMSE |
---|---|---|---|
1 | ES10 | 16.051 | [16.051, 18.746] |
2 | ES9 | 14.847 | [14.847, 16.491] |
3 | ES5 | 14.778 | [14.778, 15.741] |
4 | ES6 | 14.693 | [14.693, 15.010] |
5 | ES8 | 14.134 | [14.134, 14.244] |
6 | ES1 | 13.991 | [13.991, 14.139] |
7 | ES4 | 13.860 | [13.860, 13.970] |
8 | ES2 | 13.797 | [13.797, 14.643] |
9 | ES11 | 13.797 | [13.797, 13.943] |
10 | ES12 | 13.502 | [13.502, 13.899] |
11 | ES7 | 13.478 | [13.478, 13.893] |
12 | ES3 | 13.398 | [13.398, 13.559] |
13 | ES14 | 13.387 | [13.387, 13.523] |
14 | ES13 | 13.240 | [13.240, 13.473] |
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Wang, Q.; Huang, K.; Goh, M.; Jiao, Z.; Jia, G. Modified DEMATEL Method Based on Objective Data Grey Relational Analysis for Time Series. Systems 2023, 11, 267. https://doi.org/10.3390/systems11060267
Wang Q, Huang K, Goh M, Jiao Z, Jia G. Modified DEMATEL Method Based on Objective Data Grey Relational Analysis for Time Series. Systems. 2023; 11(6):267. https://doi.org/10.3390/systems11060267
Chicago/Turabian StyleWang, Qun, Kai Huang, Mark Goh, Zeyu Jiao, and Guozhu Jia. 2023. "Modified DEMATEL Method Based on Objective Data Grey Relational Analysis for Time Series" Systems 11, no. 6: 267. https://doi.org/10.3390/systems11060267