Holistic Approach Promotes Failure Prevention of Smart Mining Machines Based on Bayesian Networks
Abstract
:1. Introduction
1.1. Background
1.2. Fires
1.3. Aims and Objectives
2. Methodology
2.1. Degradation of Materials and Measurements
2.2. Smart Failure Prevention
2.3. Bayes’ Theorem
2.4. Hazard Detection Framework
- Identify the variables and define their states.
- Construct the BN.
- Determine prior probabilities.
- Compute conditional probability tables (CPTs).
- Infer the state of the system.
- Implementation of the BN model.
- -
- Why and how the variables were selected;
- -
- Why and how the states of each variable were determined;
- -
- How the relevant probabilities were determined and verified;
- -
- How the model was verified.
3. Results and Discussion
3.1. Measured Data from Sensor
3.2. Simulated Data
3.3. BN Results
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix B
Appendix C
- Example: Engine overheating detection module
- Step 1: Identify the Variables and Define Their States
- Engine temperature (absolute value) and CHx deviation (from normal values)
- States;
- Engine temperature: OK (Below 90 °C), low (90 °C–105 °C), medium (105 °C–120 °C), and high (Above 120 °C);
- CHx deviation: OK (Below 0.1 ppm), low (0.1 ppm–0.7 ppm), medium (0.7 ppm–1.2 ppm), and high (Above 1.2 ppm).
- Step 2: Construct the Bayesian Network (BN)
- Engine temperature (states: OK, low, medium, high)
- CHx deviation (states: OK, low, medium, high)
- Step 3: Determine Prior Probabilities
- P(Engine Overheating = OK) = 0.99
- P(Engine Overheating = low) = 0.025
- P(Engine Overheating = medium) = 0.03
- P(Engine Overheating = high = 0.001
- Step 4: Compute Conditional Probability Tables (CPTs)
- Step 5: Infer the State of the System
- Engine temperature: 110 °C = “M” state
- CHx deviation: 0.8 ppm = “M” state
- P(Engine Overheating = OK|Engine Temperature = M, CHx Deviation = M)
- P(Engine Overheating = L|Engine Temperature = M, CHx Deviation = M)
- P(Engine Overheating = M|Engine Temperature = M, CHx Deviation = M)
- P(Engine Overheating = H|Engine Temperature = M, CHx Deviation = M)
- P(Engine Overheating = OK|M, M) ∝ P(Engine Overheating = OK) × P(Engine Temperature = M|OK) × P(CHx Deviation = M|OK) ∝ 0.99 × 0.004 × 0.05 = 0.000198
- P(Engine Overheating = L|M, M) ∝ P(Engine Overheating = L) × P(Engine Temperature = M|L) × P(CHx Deviation = M|L) ∝ 0.005 × 0.02 × 0.95 = 0.0000475
- P(Engine Overheating = M|M, M) ∝ P(Engine Overheating = M) × P(Engine Temperature = M|M) × P(CHx Deviation = M|M) ∝ 0.004 × 0.97 × 0.95 = 0.01846
- P(Engine Overheating = H|M, M) ∝ P(Engine Overheating = H) × P(Engine Temperature = M|H) × P(CHx Deviation = M|H) ∝ 0.001 × 0.01 × 0.99 = 0.000000099
- Normalization constant (Z) = sum of all unnormalized probabilities
- Z = 0.000198 + 0.0000475 + 0.01846 + 0.000000099 ≈ 0.018705599
- P(Engine Overheating = OK|M, M) ≈ 0.000198/0.018705599 ≈ 0.010597
- P(Engine Overheating = L|M, M) ≈ 0.0000475/0.018705599 ≈ 0.002540
- P(Engine Overheating = M|M, M) ≈ 0.01846/0.018705599 ≈ 0.986062
- P(Engine Overheating = H|M, M) ≈ 0.000000099/0.018705599 ≈ 0.000005
- Case 1:
- P(Engine Overheating = OK) = 0.98
- P(Engine Overheating = L) = 0.01
- P(Engine Overheating = M) = 0.008
- P(Engine Overheating = H) = 0.002
- Case 2:
- P(Engine Overheating = OK) = 0.97
- P(Engine Overheating = L) = 0.015
- P(Engine Overheating = M) = 0.012
- P(Engine Overheating = H) = 0.003
- Case 3:
- P(Engine Overheating = OK) = 0.95
- P(Engine Overheating = L) = 0.025
- P(Engine Overheating = M) = 0.02
- P(Engine Overheating = H) = 0.005
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Conditional Events (P) | Probability |
---|---|
CHx: High | 0.0198 |
CHx: Low | 0.9802 |
HydraulicLeakage: Yes | 0.01 |
HydraulicLeakage: No | 0.99 |
CHx: High|HydraulicLeakage: Yes | 0.9 |
CHx: Low|HydraulicLeakage: Yes | 0.1 |
CHx: High|HydraulicLeakage: No | 0.01 |
CHx Low|HydraulicLeakage: No | 0.99 |
Parent States | Engine Temperature | CHx Measurement | |||||
---|---|---|---|---|---|---|---|
OK | L | M | H | L | M | H | |
OK | 0.99 | 0.002 | 0.004 | 0.004 | 0.95 | 0.05 | 0 |
L | 0 | 0.98 | 0.02 | 00 | 0.95 | 0.05 | 0 |
M | 0 | 0.015 | 0.97 | 0.015 | 0 | 0.95 | 0.05 |
H | 0 | 0 | 0.01 | 0.99 | 0 | 0.01 | 0.99 |
Engine Overheating | Cable Overheating | Hydraulic Leakage | Brake Leakage | |||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 Temp. | CHx | Temp. | CHx | Oil Level | CHx | Pressure | 1 Temp. | |||||||||||||||
Case | OK | L | M | H | L | M | H | OK | L | M | H | L | M | H | OK | Leak | L | H | OK | 2 NK | OK | 2 NK |
1 | x | x | ||||||||||||||||||||
2 | x | x | ||||||||||||||||||||
3 | x | x | ||||||||||||||||||||
4 | x | x | ||||||||||||||||||||
5 | x | x | ||||||||||||||||||||
6 | x | x | ||||||||||||||||||||
7 | x | x | ||||||||||||||||||||
8 | x | x | ||||||||||||||||||||
9 | x | x | ||||||||||||||||||||
10 | x | x | ||||||||||||||||||||
11 | x | x | ||||||||||||||||||||
12 | x | x |
Engine Overheating | Cable Overheating | Hydraulic Leakage | Brake Leakage | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Case | OK | L | M | H | OK | L | M | H | NO | YES | NO | YES |
1 | 100 | 0 | 0 | 0 | ||||||||
2 | 34.95 | 65.05 | 0 | 0 | ||||||||
3 | 7.88 | 0.16 | 91.96 | 0 | ||||||||
4 | 0 | 0 | 0.16 | 99.84 | ||||||||
5 | 100 | 0 | 0 | 0 | ||||||||
6 | 44.32 | 55.68 | 0 | 0 | ||||||||
7 | 7.8 | 0.11 | 92.09 | 0 | ||||||||
8 | 0.08 | 99.92 | ||||||||||
9 | 100 | 0 | ||||||||||
10 | 1.1 | 98.9 | ||||||||||
11 | 100 | 0 | ||||||||||
12 | 1 | 99 |
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Martinsen, M.; Fentaye, A.D.; Dahlquist, E.; Zhou, Y. Holistic Approach Promotes Failure Prevention of Smart Mining Machines Based on Bayesian Networks. Machines 2023, 11, 940. https://doi.org/10.3390/machines11100940
Martinsen M, Fentaye AD, Dahlquist E, Zhou Y. Holistic Approach Promotes Failure Prevention of Smart Mining Machines Based on Bayesian Networks. Machines. 2023; 11(10):940. https://doi.org/10.3390/machines11100940
Chicago/Turabian StyleMartinsen, Madeleine, Amare Desalegn Fentaye, Erik Dahlquist, and Yuanye Zhou. 2023. "Holistic Approach Promotes Failure Prevention of Smart Mining Machines Based on Bayesian Networks" Machines 11, no. 10: 940. https://doi.org/10.3390/machines11100940
APA StyleMartinsen, M., Fentaye, A. D., Dahlquist, E., & Zhou, Y. (2023). Holistic Approach Promotes Failure Prevention of Smart Mining Machines Based on Bayesian Networks. Machines, 11(10), 940. https://doi.org/10.3390/machines11100940