Improved Honey Badger Algorithm Based on Elite Tangent Search and Differential Mutation with Applications in Fault Diagnosis
Abstract
:1. Introduction
- (1)
- The development of the IHBA addresses the key shortcomings of the original HBA by enhancing exploration and accelerating convergence.
- (2)
- The successful application of the IHBA in motor bearing fault diagnosis, providing a novel approach to improving fault detection accuracy in industrial settings.
2. Honey Badger Algorithm (HBA)
3. Improved Honey Badger Algorithm (IHBA)
3.1. Cubic Chaotic Mapping
Algorithm 1: Population filtering mechanism |
Initialization of honey badger population size ; 1. Use Equation (9) to generate a population with solutions with random positions; 2. Calculate the fitness function value for each solutions; 3. Sort all individuals according to their fitness function values in descending order; 7. Return . |
3.2. Random Value Perturbation Strategy
3.3. Elite Tangent Search and Differential Mutation Strategy
Algorithm 2: Pseudocode of the IHBA. |
Input: |
Set honey badger population size ; |
Maximum number of iterations ; |
Dimension ; |
Lower bound , upper bound ; |
Set parameters: constant , attraction factor ; |
Output: |
: Global best fitness; |
: Position of the global best individual; |
1. Initialize the population using Algorithm 1; |
2. Evaluate the fitness of each honey badger position using objective function and assign to , [1, 2, …, Ns]; |
3. Save best position and assign fitness to ; |
4. while do |
5. Update the decreasing factor using Equation (5); |
6. For to do |
7. Calculate the intensity using Equation (2); |
8. Compute the adaptation parameter using Equation (10); |
9. if then |
10. if then 11. Update the position using Equation (11), Select a random individual instead of the globally optimal ; 12. else |
13. Update the position using Equation (12); 14. end if |
15. else |
16. if then 17. Update the position using Equation (6); 18. else 19. Update the position using Equation (8); 20. end if |
21. end if 22. Evaluate the new individual and assign to the fitness ; 23. if then 24. Set and ; 25. end if 26. if then 27. Set and ; 28. end if 29. if remains unchanged for three consecutive iterations, then execute the elite tangent and differential mutation strategies then 30. Sort the population fitness in ascending order; 31. Divide the population into two groups (optimal half) as elite subgroups and after as exploration subgroups); 32. for to do 33. Generate a random angle θ in the range [0, π/2.1]; 34. Calculate the step size using Equation (14); 35. if == then 36. Update the position using Equation (13(a)); 37. else 38. Update the position using Equation (13(b)); 39. end if 40. end for 41. for to do 42. Randomly select three distinct individuals rand1, rand2, rand3 from the population; 43. Update the position using Equation (15); 44. end for 45. end if 46. if then 47. Set and ; 48. end if 49. if then 50. Set = and ; 51. end if |
52. end for |
53. end while Stop criteria satisfied. |
54. Return , . |
4. Experiment and Results
4.1. Test Function
4.2. Results and Discussions
4.2.1. CEC2017 Test Function Set Optimization Experiment
4.2.2. Wilcoxon Rank Sum Test
4.2.3. CEC2017 Convergence Curve of the Test Function Set
5. Engineering Optimization
5.1. Optimizing the Parameters of VMD
5.2. Rolling Bearing Fault Diagnosis
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Algorithm | Parameter Setting |
COA | decreases linearly from 2 to 0, |
DBO | , , , , |
OCSSA | , , , |
BWO | is probability of whale fall decreased at interval [0.1, 0.05] |
OOA | are random numbers at interval [0, 1], are random numbers from the set {1, 2} |
HHO | variable changes from −1 to 1, |
HBA | , |
IHBA | , , |
Type | No. | Function | D | Initial Range | |
---|---|---|---|---|---|
Unimodal function | Shifted and rotated Bent Cigar Function | 30 | 100 | ||
Shifted and rotated Zakharov Function | 30 | 300 | |||
Simple multimodal function | Shifted and rotated Rosenbrock Function | 30 | 400 | ||
Shifted and rotated Lunacek Bi-Rastrigin Function | 30 | 700 | |||
Shifted and rotated Non-Continuous Rastrigin Function | 30 | 800 | |||
Shifted and rotated Levy Function | 30 | 900 | |||
Hybrid function | Hybrid Function 3 (N = 3) | 30 | 1300 | ||
Hybrid Function 4 (N = 4) | 30 | 1400 | |||
Hybrid Function 5 (N = 4) | 30 | 1500 | |||
Hybrid Function 6 (N = 4) | 30 | 1600 | |||
Composition function | Composition Function 1 (N = 3) | 30 | 2100 | ||
Composition Function 3 (N = 4) | 30 | 2200 |
Fun. | D | Meas. | IHBA | OCSSA | HBA | HHO | BWO | OOA | DBO | COA |
---|---|---|---|---|---|---|---|---|---|---|
10 | Best | 1.00 × 102 | 1.04 × 102 | 1.33 × 102 | 1.90 × 105 | 4.39 × 109 | 1.55 × 109 | 1.84 × 108 | 4.24 × 109 | |
Std | 2.47 × 103 | 2.22 × 103 | 3.50 × 103 | 3.01 × 105 | 3.83 × 109 | 2.74 × 109 | 5.45 × 108 | 2.86 × 109 | ||
Ave | 2.06 × 103 | 3.04 × 103 | 3.44 × 103 | 6.90 × 105 | 1.42 × 1010 | 8.21 × 109 | 1.18 × 109 | 8.15 × 109 | ||
30 | Best | 6.43 × 102 | 1.37 × 104 | 3.95 × 103 | 4.24 × 107 | 5.48 × 1010 | 3.27 × 1010 | 2.04 × 1010 | 3.51 × 1010 | |
Std | 4.83 × 105 | 3.60 × 105 | 8.40 × 105 | 3.74 × 107 | 4.97 × 109 | 7.04 × 109 | 3.73 × 109 | 7.54 × 109 | ||
Ave | 1.31 × 105 | 2.35 × 105 | 2.06 × 105 | 8.84 × 107 | 6.77 × 1010 | 5.12 × 1010 | 2.74 × 1010 | 5.29 × 1010 | ||
50 | Best | 1.57 × 106 | 6.12 × 107 | 6.91 × 106 | 7.22 × 108 | 1.10 × 1011 | 8.76 × 1010 | 5.97 × 1010 | 8.83 × 1010 | |
Std | 1.57 × 107 | 9.29 × 107 | 3.67 × 108 | 7.45 × 108 | 5.55 × 109 | 8.24 × 109 | 5.36 × 109 | 8.32 × 109 | ||
Ave | 2.06 × 107 | 2.07 × 108 | 2.54 × 108 | 1.55 × 109 | 1.22 × 1011 | 1.09 × 1011 | 6.90 × 1010 | 1.09 × 1011 | ||
10 | Best | 3.00 × 102 | 3.00 × 102 | 3.00 × 102 | 3.02 × 102 | 7.61 × 103 | 4.45 × 103 | 5.01 × 102 | 3.65 × 103 | |
Std | 2.68 × 10−7 | 3.99 × 10−3 | 3.05 × 10−5 | 5.33 × 101 | 1.93 × 103 | 3.05 × 103 | 1.49 × 103 | 2.94 × 103 | ||
Ave | 3.00 × 102 | 3.00 × 102 | 3.00 × 102 | 3.40 × 102 | 1.19 × 104 | 1.22 × 104 | 3.28 × 103 | 9.47 × 103 | ||
30 | Best | 2.00 × 103 | 2.76 × 104 | 1.33 × 104 | 3.18 × 104 | 6.91 × 104 | 6.90 × 104 | 6.50 × 104 | 6.52 × 104 | |
Std | 3.10 × 103 | 8.38 × 103 | 6.84 × 103 | 7.26 × 103 | 1.08 × 104 | 7.71 × 103 | 9.02 × 103 | 7.46 × 103 | ||
Ave | 5.86 × 103 | 4.19 × 104 | 2.76 × 104 | 4.45 × 104 | 9.32 × 104 | 8.49 × 104 | 8.17 × 104 | 8.50 × 104 | ||
50 | Best | 4.52 × 104 | 1.33 × 105 | 7.60 × 104 | 1.17 × 105 | 1.73 × 105 | 1.34 × 105 | 1.68 × 105 | 1.63 × 105 | |
Std | 1.29 × 104 | 2.85 × 104 | 2.29 × 104 | 1.71 × 104 | 2.32 × 104 | 3.18 × 104 | 4.48 × 104 | 1.58 × 104 | ||
Ave | 6.48 × 104 | 1.85 × 105 | 1.24 × 105 | 1.51 × 105 | 2.13 × 105 | 2.12 × 105 | 2.26 × 105 | 1.92 × 105 | ||
10 | Best | 4.00 × 102 | 4.00 × 102 | 4.00 × 102 | 4.00 × 102 | 8.44 × 102 | 4.80 × 102 | 4.40 × 102 | 6.21 × 102 | |
Std | 5.54 × 10−1 | 2.23 × 101 | 1.43 | 3.93 × 101 | 4.47 × 102 | 2.71 × 102 | 2.68 × 101 | 3.24 × 102 | ||
Ave | 4.01 × 102 | 4.12 × 102 | 4.02 × 102 | 4.31 × 102 | 1.62 × 103 | 8.58 × 102 | 4.82 × 102 | 9.58 × 102 | ||
30 | Best | 4.10 × 102 | 4.74 × 102 | 4.46 × 102 | 5.08 × 102 | 1.11 × 104 | 8.30 × 103 | 3.16 × 103 | 7.46 × 103 | |
Std | 2.79 × 101 | 2.44 × 101 | 2.33 × 101 | 5.66 × 101 | 2.44 × 103 | 2.78 × 103 | 1.93 × 103 | 2.89 × 103 | ||
Ave | 4.99 × 102 | 5.10 × 102 | 5.01 × 102 | 6.06 × 102 | 1.70 × 104 | 1.33 × 104 | 6.37 × 103 | 1.37 × 104 | ||
50 | Best | 5.27 × 102 | 5.13 × 102 | 4.81 × 102 | 7.24 × 102 | 4.08 × 104 | 1.79 × 104 | 1.34 × 104 | 2.48 × 104 | |
Std | 5.48 × 101 | 6.64 × 101 | 8.01 × 101 | 2.19 × 102 | 3.10 × 103 | 7.04 × 103 | 2.08 × 103 | 5.95 × 103 | ||
Ave | 6.09 × 102 | 6.22 × 102 | 6.47 × 102 | 1.14 × 103 | 4.61 × 104 | 3.50 × 104 | 1.70 × 104 | 3.62 × 104 | ||
10 | Best | 7.15 × 102 | 7.24 × 102 | 7.19 × 102 | 7.54 × 102 | 8.09 × 102 | 7.56 × 102 | 7.61 × 102 | 7.62 × 102 | |
Std | 4.71 | 2.59 × 101 | 9.86 | 1.38 × 101 | 8.72 | 1.82 × 101 | 1.06 × 101 | 1.84 × 101 | ||
Ave | 7.23 × 102 | 7.62 × 102 | 7.32 × 102 | 7.84 × 102 | 8.30 × 102 | 7.90 × 102 | 7.80 × 102 | 7.95 × 102 | ||
30 | Best | 7.58 × 102 | 8.58 × 102 | 8.32 × 102 | 1.12 × 103 | 1.33 × 103 | 1.26 × 103 | 1.11 × 103 | 1.27 × 103 | |
Std | 2.89 × 101 | 1.51 × 102 | 5.24 × 101 | 6.52 × 101 | 3.57 × 101 | 6.42 × 101 | 3.43 × 101 | 5.49 × 101 | ||
Ave | 8.00 × 102 | 1.09 × 103 | 9.10 × 102 | 1.29 × 103 | 1.47 × 103 | 1.39 × 103 | 1.20 × 103 | 1.42 × 103 | ||
50 | Best | 8.69 × 102 | 1.08 × 103 | 1.02 × 103 | 1.66 × 103 | 1.99 × 103 | 1.81 × 103 | 1.58 × 103 | 1.88 × 103 | |
Std | 4.44 × 101 | 1.92 × 102 | 1.12 × 102 | 8.83 × 101 | 3.14 × 101 | 9.47 × 101 | 6.95 × 101 | 7.10 × 101 | ||
Ave | 9.40 × 102 | 1.56 × 103 | 1.20 × 103 | 1.86 × 103 | 2.09 × 103 | 2.01 × 103 | 1.76 × 103 | 2.03 × 103 | ||
10 | Best | 8.01 × 102 | 8.19 × 102 | 8.09 × 102 | 8.11 × 102 | 8.41 × 102 | 8.21 × 102 | 8.26 × 102 | 8.32 × 102 | |
Std | 5.92 | 9.05 | 6.26 | 8.85 | 5.95 | 9.22 | 5.87 | 9.20 | ||
Ave | 8.12 × 102 | 8.35 × 102 | 8.18 × 102 | 8.29 × 102 | 8.54 × 102 | 8.49 × 102 | 8.35 × 102 | 8.54 × 102 | ||
30 | Best | 8.28 × 102 | 9.13 × 102 | 8.42 × 102 | 9.32 × 102 | 1.13 × 103 | 1.08 × 103 | 1.01 × 103 | 1.05 × 103 | |
Std | 1.63 × 101 | 3.15 × 101 | 2.45 × 101 | 2.35 × 101 | 1.58 × 101 | 2.49 × 101 | 2.44 × 101 | 2.62 × 101 | ||
Ave | 8.51 × 102 | 9.70 × 102 | 8.96 × 102 | 9.78 × 102 | 1.16 × 103 | 1.12 × 103 | 1.06 × 103 | 1.13 × 103 | ||
50 | Best | 8.72 × 102 | 1.08 × 103 | 9.88 × 102 | 1.14 × 103 | 1.48 × 103 | 1.42 × 103 | 1.31 × 103 | 1.40 × 103 | |
Std | 3.79 × 101 | 4.42 × 101 | 3.56 × 101 | 3.69 × 101 | 2.25 × 101 | 3.28 × 101 | 4.06 × 101 | 3.48 × 101 | ||
Ave | 9.40 × 102 | 1.15 × 103 | 1.05 × 103 | 1.21 × 103 | 1.52 × 103 | 1.47 × 103 | 1.39 × 103 | 1.48 × 103 | ||
10 | Best | 9.00 × 102 | 9.00 × 102 | 9.00 × 102 | 1.12 × 103 | 1.45 × 103 | 9.77 × 102 | 9.53 × 102 | 1.04 × 103 | |
Std | 2.27 × 10−2 | 1.60 × 102 | 2.51 | 2.00 × 102 | 1.28 × 102 | 1.89 × 102 | 9.49 × 101 | 2.18 × 102 | ||
Ave | 9.00 × 102 | 1.01 × 103 | 9.01 × 102 | 1.50 × 103 | 1.80 × 103 | 1.34 × 103 | 1.06 × 103 | 1.41 × 103 | ||
30 | Best | 9.06 × 102 | 2.81 × 103 | 1.06 × 103 | 5.72 × 103 | 9.35 × 103 | 5.84 × 103 | 4.57 × 103 | 4.95 × 103 | |
Std | 5.99 × 101 | 7.57 × 102 | 9.18 × 102 | 9.25 × 102 | 7.96 × 102 | 1.21 × 103 | 1.45 × 103 | 1.80 × 103 | ||
Ave | 9.76 × 102 | 5.07 × 103 | 2.60 × 103 | 7.93 × 103 | 1.12 × 104 | 9.17 × 103 | 7.86 × 103 | 9.92 × 103 | ||
50 | Best | 1.14 × 103 | 8.28 × 103 | 4.60 × 103 | 1.89 × 104 | 3.37 × 104 | 2.94 × 104 | 2.14 × 104 | 2.76 × 104 | |
Std | 4.02 × 102 | 1.99 × 103 | 4.17 × 103 | 3.87 × 103 | 2.16 × 103 | 3.04 × 103 | 3.95 × 103 | 3.69 × 103 | ||
Ave | 1.80 × 103 | 1.32 × 104 | 1.01 × 104 | 2.88 × 104 | 3.82 × 104 | 3.40 × 104 | 3.13 × 104 | 3.45 × 104 | ||
10 | Best | 1.31 × 103 | 2.23 × 103 | 1.48 × 103 | 2.11 × 103 | 3.57 × 105 | 2.37 × 103 | 2.81 × 103 | 2.44 × 103 | |
Std | 1.07 × 102 | 3.09 × 103 | 1.27 × 104 | 1.34 × 104 | 2.02 × 107 | 1.23 × 104 | 1.63 × 104 | 6.92 × 103 | ||
Ave | 1.38 × 103 | 1.46 × 104 | 9.24 × 103 | 1.49 × 104 | 1.59 × 107 | 1.36 × 104 | 2.39 × 104 | 1.05 × 104 | ||
30 | Best | 3.01 × 103 | 5.12 × 103 | 7.38 × 103 | 2.78 × 105 | 7.33 × 109 | 9.86 × 108 | 2.11 × 108 | 7.82 × 108 | |
Std | 2.58 × 104 | 4.25 × 104 | 3.56 × 104 | 7.35 × 105 | 4.41 × 109 | 3.69 × 109 | 1.13 × 109 | 3.70 × 109 | ||
Ave | 3.16 × 104 | 3.43 × 104 | 4.35 × 104 | 9.50 × 105 | 1.50 × 109 | 7.00 × 109 | 1.83 × 109 | 6.95 × 109 | ||
50 | Best | 4.63 × 103 | 1.35 × 104 | 1.25 × 104 | 3.23 × 106 | 4.73 × 1010 | 2.48 × 1010 | 3.42 × 109 | 1.80 × 1010 | |
Std | 1.51 × 104 | 4.75 × 104 | 6.52 × 104 | 9.01 × 106 | 1.21 × 1010 | 1.19 × 1010 | 5.57 × 109 | 1.07 × 1010 | ||
Ave | 2.10 × 104 | 7.86 × 104 | 6.94 × 104 | 9.69 × 106 | 6.67 × 1010 | 4.58 × 1010 | 1.23 × 1010 | 3.84 × 1010 | ||
10 | Best | 1.40 × 103 | 1.43 × 103 | 1.44 × 103 | 1.48 × 103 | 1.57 × 103 | 1.45 × 103 | 1.52 × 103 | 1.46 × 103 | |
Std | 7.90 | 6.85 × 101 | 5.64 × 101 | 3.82 × 102 | 2.01 × 102 | 2.11 × 103 | 7.10 × 102 | 3.35 × 101 | ||
Ave | 1.42 × 103 | 1.50 × 103 | 1.52 × 103 | 1.68 × 103 | 1.80 × 103 | 2.55 × 103 | 2.15 × 103 | 1.51 × 103 | ||
30 | Best | 1.56 × 103 | 5.38 × 103 | 2.72 × 103 | 6.68 × 103 | 3.15 × 106 | 1.28 × 105 | 5.56 × 104 | 1.41 × 105 | |
Std | 2.15 × 103 | 3.40 × 104 | 1.95 × 104 | 7.07 × 105 | 7.65 × 106 | 2.50 × 106 | 4.64 × 105 | 1.95 × 106 | ||
Ave | 2.65 × 103 | 4.87 × 104 | 2.67 × 104 | 7.96 × 105 | 1.33 × 107 | 2.56 × 106 | 5.94 × 105 | 2.08 × 106 | ||
50 | Best | 6.85 × 103 | 1.20 × 105 | 3.17 × 104 | 1.81 × 105 | 5.03 × 107 | 1.29 × 107 | 4.76 × 105 | 5.02 × 106 | |
Std | 5.38 × 104 | 3.67 × 105 | 5.14 × 105 | 1.97 × 106 | 1.28 × 108 | 6.41 × 107 | 7.42 × 106 | 2.87 × 107 | ||
Ave | 6.27 × 104 | 4.96 × 105 | 2.50 × 105 | 3.06 × 106 | 2.32 × 108 | 9.59 × 107 | 8.46 × 106 | 4.63 × 107 | ||
10 | Best | 1.50 × 103 | 1.63 × 103 | 1.56 × 108 | 2.05 × 103 | 3.15 × 103 | 1.82 × 103 | 1.94 × 103 | 1.69 × 103 | |
Std | 4.82 × 101 | 7.73 × 102 | 9.54 × 102 | 3.02 × 103 | 2.18 × 103 | 4.54 × 103 | 1.64 × 103 | 2.89 × 103 | ||
Ave | 1.53 × 103 | 2.22 × 103 | 1.84 × 103 | 6.58 × 103 | 8.69 × 103 | 1.12 × 104 | 4.08 × 103 | 4.61 × 103 | ||
30 | Best | 1.68 × 103 | 2.04 × 103 | 1.96 × 103 | 3.37 × 104 | 8.99 × 107 | 5.54 × 106 | 3.61 × 105 | 4.78 × 106 | |
Std | 1.36 × 104 | 1.42 × 104 | 1.64 × 104 | 4.89 × 104 | 4.60 × 108 | 4.38 × 108 | 4.89 × 106 | 4.02 × 108 | ||
Ave | 1.21 × 104 | 9.61 × 103 | 1.91 × 104 | 9.07 × 104 | 1.04 × 109 | 3.83 × 108 | 4.59 × 106 | 4.11 × 108 | ||
50 | Best | 2.12 × 103 | 5.89 × 103 | 6.06 × 103 | 2.73 × 105 | 8.59 × 109 | 2.38 × 109 | 1.38 × 108 | 1.44 × 109 | |
Std | 9.93 × 103 | 2.09 × 104 | 1.18 × 104 | 4.41 × 105 | 2.76 × 109 | 2.96 × 109 | 9.10 × 108 | 3.29 × 109 | ||
Ave | 1.44 × 104 | 3.71 × 104 | 2.51 × 104 | 9.50 × 105 | 1.36 × 1010 | 7.64 × 109 | 1.62 × 109 | 7.90 × 109 | ||
10 | Best | 1.60 × 103 | 1.60 × 103 | 1.60 × 103 | 1.61 × 103 | 1.92 × 103 | 1.71 × 103 | 1.63 × 103 | 1.70 × 103 | |
Std | 5.54 × 101 | 1.89 × 102 | 1.00 × 102 | 1.44 × 102 | 1.05 × 102 | 1.38 × 102 | 9.35 × 101 | 1.34 × 102 | ||
Ave | 1.64 × 103 | 1.98 × 103 | 1.73 × 103 | 1.87 × 103 | 2.19 × 103 | 1.97 × 103 | 1.78 × 103 | 1.97 × 103 | ||
30 | Best | 1.75 × 103 | 1.99 × 103 | 1.75 × 103 | 2.67 × 103 | 6.00 × 103 | 3.90 × 103 | 3.53 × 103 | 3.76 × 103 | |
Std | 3.30 × 102 | 3.83 × 102 | 5.68 × 102 | 4.91 × 102 | 1.78 × 103 | 6.78 × 102 | 2.71 × 102 | 8.40 × 102 | ||
Ave | 2.35 × 103 | 2.80 × 103 | 2.72 × 103 | 3.56 × 103 | 8.39 × 103 | 5.11 × 103 | 3.98 × 103 | 5.35 × 103 | ||
50 | Best | 2.15 × 103 | 2.58 × 103 | 2.41 × 103 | 3.52 × 103 | 7.75 × 103 | 6.51 × 103 | 4.62 × 103 | 6.26 × 103 | |
Std | 5.67 × 102 | 4.11 × 102 | 4.60 × 102 | 7.80 × 102 | 1.74 × 103 | 1.20 × 103 | 5.28 × 102 | 1.53 × 103 | ||
Ave | 3.25 × 103 | 3.64 × 103 | 3.46 × 103 | 4.67 × 103 | 1.19 × 104 | 8.41 × 103 | 5.64 × 103 | 8.81 × 103 | ||
10 | Best | 2.20 × 103 | 2.20 × 103 | 2.20 × 103 | 2.20 × 103 | 2.23 × 103 | 2.23 × 103 | 2.21 × 103 | 2.23 × 103 | |
Std | 5.51 × 101 | 6.09 × 101 | 5.52 × 101 | 6.24 × 101 | 5.45 × 101 | 4.93 × 101 | 8.33 | 4.44 × 101 | ||
Ave | 2.27 × 103 | 2.31 × 103 | 2.28 × 103 | 2.33 × 103 | 2.31 × 103 | 2.33 × 103 | 2.22 × 103 | 2.35 × 103 | ||
30 | Best | 2.33 × 103 | 2.20 × 103 | 2.36 × 103 | 2.48 × 103 | 2.58 × 103 | 2.58 × 103 | 2.33 × 103 | 2.64 × 103 | |
Std | 1.39 × 101 | 1.51 × 102 | 3.11 × 101 | 4.27 × 101 | 6.86 × 101 | 4.73 × 101 | 9.83 × 101 | 4.01 × 101 | ||
Ave | 2.35 × 103 | 2.33 × 103 | 2.40 × 103 | 2.57 × 103 | 2.70 × 103 | 2.69 × 103 | 2.53 × 103 | 2.71 × 103 | ||
50 | Best | 2.37 × 103 | 2.49 × 103 | 2.41 × 103 | 2.72 × 103 | 3.16 × 103 | 3.02 × 103 | 2.89 × 103 | 3.08 × 103 | |
Std | 2.41 × 101 | 6.94 × 101 | 4.49 × 101 | 9.14 × 101 | 8.19 × 101 | 5.92 × 101 | 4.68 × 101 | 8.02 × 101 | ||
Ave | 2.41 × 103 | 2.63 × 103 | 2.52 × 103 | 2.91 × 103 | 3.30 × 103 | 3.13 × 103 | 2.97 × 103 | 3.20 × 103 | ||
10 | Best | 2.60 × 103 | 2.61 × 103 | 2.61 × 103 | 2.61 × 103 | 2.66 × 103 | 2.66 × 103 | 2.63 × 103 | 2.66 × 103 | |
Std | 9.08 | 1.00 × 101 | 1.47 × 101 | 2.91 × 101 | 2.94 × 101 | 2.21 × 101 | 1.73 × 101 | 2.55 × 101 | ||
Ave | 2.62 × 103 | 2.62 × 103 | 2.62 × 103 | 2.66 × 103 | 2.73 × 103 | 2.69 × 103 | 2.66 × 103 | 2.69 × 103 | ||
30 | Best | 2.66 × 103 | 2.75 × 103 | 2.73 × 103 | 3.04 × 103 | 3.54 × 103 | 3.27 × 103 | 3.03 × 103 | 3.25 × 103 | |
Std | 2.27 × 101 | 7.59 × 101 | 3.53 × 101 | 1.22 × 102 | 1.97 × 102 | 1.53 × 102 | 9.57 × 101 | 1.16 × 102 | ||
Ave | 2.71 × 103 | 2.85 × 103 | 2.79 × 103 | 3.20 × 103 | 3.84 × 103 | 3.59 × 103 | 3.16 × 103 | 3.49 × 103 | ||
50 | Best | 2.80 × 103 | 2.97 × 103 | 2.88 × 103 | 3.51 × 103 | 4.58 × 103 | 3.97 × 103 | 3.51 × 103 | 4.12 × 103 | |
Std | 3.64 × 101 | 1.11 × 102 | 7.79 × 101 | 1.82 × 102 | 1.44 × 102 | 2.02 × 102 | 1.65 × 102 | 1.72 × 102 | ||
Ave | 2.87 × 103 | 3.14 × 103 | 3.02 × 103 | 3.85 × 103 | 4.83 × 103 | 4.50 × 103 | 3.84 × 103 | 4.40 × 103 |
Fun. | |||||||||
Dim. | 10 | 30 | 50 | 10 | 30 | 50 | 10 | 30 | 50 |
IHBA | 7.86 × 10−2 | 1.02 × 10−1 | 1.40 × 10−1 | 7.37 × 10−2 | 1.16 × 10−1 | 1.61 × 10−1 | 6.99 × 10−2 | 9.70 × 10−2 | 1.37 × 10−1 |
HBA | 6.05 × 10−2 | 8.30 × 10−2 | 1.18 × 10−1 | 5.81 × 10−2 | 8.28 × 10−2 | 1.19 × 10−1 | 5.87 × 10−2 | 8.29 × 10−2 | 1.18 × 10−1 |
Fun. | |||||||||
Dim. | 10 | 30 | 50 | 10 | 30 | 50 | 10 | 30 | 50 |
IHBA | 9.24 × 10−2 | 1.33 × 10−1 | 1.85 × 10−1 | 9.25 × 10−2 | 1.36 × 10−1 | 1.81 × 10−1 | 8.80 × 10−2 | 1.40 × 10−1 | 2.06 × 10−1 |
HBA | 6.79 × 10−2 | 1.02 × 10−1 | 1.46 × 10−1 | 6.47 × 10−2 | 1.02 × 10−1 | 1.45 × 10−1 | 6.78 × 10−2 | 1.05 × 10−1 | 1.46 × 10−1 |
Fun. | |||||||||
Dim. | 10 | 30 | 50 | 10 | 30 | 50 | 10 | 30 | 50 |
IHBA | 8.65 × 10−2 | 1.11 × 10−1 | 1.51 × 10−1 | 9.46 × 10−2 | 1.45 × 10−1 | 1.98 × 10−1 | 8.57 × 10−2 | 1.08 × 10−1 | 1.45 × 10−1 |
HBA | 6.37 × 10−2 | 9.54 × 10−2 | 1.37 × 10−1 | 6.71 × 10−2 | 1.11 × 10−1 | 1.62 × 10−1 | 6.07 × 10−2 | 9.08 × 10−2 | 1.27 × 10−1 |
Fun. | |||||||||
Dim. | 10 | 30 | 50 | 10 | 30 | 50 | 10 | 30 | 50 |
IHBA | 9.42 × 10−2 | 1.31 × 10−1 | 1.81 × 10−1 | 1.04 × 10−1 | 1.89 × 10−1 | 3.01 × 10−1 | 1.26 × 10−1 | 2.16 × 10−1 | 3.66 × 10−1 |
HBA | 6.36 × 10−2 | 9.92 × 10−2 | 1.39 × 10−1 | 7.96 × 10−2 | 1.47 × 10−1 | 2.38 × 10−1 | 9.06 × 10−2 | 1.72 × 10−1 | 2.91 × 10−1 |
Function | OCSSA | HBA | HHO | BWO | OOA | DBO | COA |
---|---|---|---|---|---|---|---|
f1 | 7.48 × 10−2 | 8.50 × 10−2 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 |
f3 | 3.69 × 10−11 | 2.03 × 10−7 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 |
f4 | 1.17 × 10−4 | 5.09 × 10−6 | 6.12 × 10−10 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 |
f7 | 1.46 × 10−10 | 5.97 × 10−5 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 |
f8 | 6.67 × 10−11 | 5.40 × 10−4 | 1.69 × 10−9 | 3.02 × 10−11 | 3.33 × 10−11 | 3.33 × 10−11 | 3.02 × 10−11 |
f9 | 1.05 × 10−9 | 7.16 × 10−9 | 2.74 × 10−11 | 2.74 × 10−11 | 2.74 × 10−11 | 2.74 × 10−11 | 2.74 × 10−11 |
f13 | 3.02 × 10−11 | 4.08 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 |
f14 | 3.34 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 |
f15 | 6.70 × 10−11 | 2.23 × 10−9 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.02 × 10−11 | 3.34 × 10−11 |
f16 | 4.69 × 10−8 | 1.87 × 10−5 | 9.26 × 10−9 | 3.02 × 10−11 | 8.99 × 10−11 | 4.69 × 10−8 | 6.07 × 10−11 |
f21 | 1.34 × 10−5 | 6.79 × 10−2 | 3.09 × 10−6 | 1.63 × 10−2 | 2.00 × 10−5 | 1.86 × 10−1 | 2.20 × 10−7 |
f23 | 4.98 × 10−4 | 1.68 × 10−3 | 2.19 × 10−8 | 3.02 × 10−11 | 3.02 × 10−11 | 1.09 × 10−10 | 3.02 × 10−11 |
Fault Type | Normal | Inner Ring Fault | Rolling Ball Fault | Outer Ring Fault | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Fault label | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Fault diameter (d/inch) | - | 0.007 | 0.014 | 0.021 | 0.007 | 0.014 | 0.021 | 0.007 | 0.014 | 0.021 |
Training sample | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 | 90 |
Test sample | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 | 30 |
Sample data size | 2048 | 2048 | 2048 | 2048 | 2048 | 2048 | 2048 | 2048 | 2048 | 2048 |
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Ting, H.; Yong, C.; Peng, C. Improved Honey Badger Algorithm Based on Elite Tangent Search and Differential Mutation with Applications in Fault Diagnosis. Processes 2025, 13, 256. https://doi.org/10.3390/pr13010256
Ting H, Yong C, Peng C. Improved Honey Badger Algorithm Based on Elite Tangent Search and Differential Mutation with Applications in Fault Diagnosis. Processes. 2025; 13(1):256. https://doi.org/10.3390/pr13010256
Chicago/Turabian StyleTing, He, Chang Yong, and Chen Peng. 2025. "Improved Honey Badger Algorithm Based on Elite Tangent Search and Differential Mutation with Applications in Fault Diagnosis" Processes 13, no. 1: 256. https://doi.org/10.3390/pr13010256
APA StyleTing, H., Yong, C., & Peng, C. (2025). Improved Honey Badger Algorithm Based on Elite Tangent Search and Differential Mutation with Applications in Fault Diagnosis. Processes, 13(1), 256. https://doi.org/10.3390/pr13010256