The paradigm of complex probability and analytic nonlinear prognostic for vehicle suspension systems

Figures & data

Figure 1. The diagram of the principal objectives of this research work.

Figure 2. Chf, DOK, and Pc for the uniform probability distribution in 2D.

Figure 3. DOK, Chf, and Pc for the uniform probability distribution in 3D with .

Figure 4. Graph of for any distribution

Figure 5. Graph of for any distribution.

Figure 6. MChf, DOK, and Pc for the uniform probability distribution in 2D.

Figure 7. DOK, MChf, and Pc for the uniform probability distribution in 3D with .

Figure 8. Chf and MChf for the uniform probability distribution in 2D.

Figure 9. Chf and MChf for the uniform probability distribution in 3D with MChf + Chf = 0.

Figure 10. Chf, MChf, DOK, and Pc for the uniform probability distribution in 2D.

Figure 11. The EKA or the CPP diagram.

Figure 12. The nonlinear law of damage.

Figure 13. CPP and the prognostic of degradation.

Figure 14. The prognostic of RUL.

Figure 15. P_r, degradation, and the CDF step function.

Figure 16. P_r as a function of Degradation D(N).

Figure 17. Degradation and P_r.

Figure 18. P_r, D, and RUL.

Figure 19. Suspension degradation under nonlinear damage law for severe mode of road excitation.

Figure 20. Suspension RUL as a function of degradation for severe mode of road excitation.

Figure 21. Degradation and CPP parameters for mode 1.

Figure 22. Degradation and CPP parameters with MChf for mode 1.

Figure 23. Degradation, rescaled RUL, and CPP parameters for mode 1.

Figure 24. Degradation, rescaled RUL, and CPP parameters with MChf for mode 1.

Figure 25. DOK and Chf in terms of N and of each other for mode 1.

Figure 26. P_r and P_m/i in terms of N and of each other for mode 1.

Figure 27. The complex probability vector Z in terms of N for mode 1.

Figure 28. Suspension degradation under nonlinear damage law for fair mode of road excitation.

Figure 29. Suspension RUL as a function of degradation for fair mode of road excitation.

Figure 30. Degradation and CPP parameters for mode 2.

Figure 31. Degradation and CPP parameters with MChf for mode 2.

Figure 32. Degradation, rescaled RUL, and CPP parameters for mode 2.

Figure 33. Degradation, rescaled RUL, and CPP parameters with MChf for mode 2.

Figure 34. DOK and Chf in terms of N and of each other for mode 2.

Figure 35. P_r and P_m/i in terms of N and of each other for mode 2.

Figure 36. The complex probability vector Z in terms of N for mode 2.

Figure 37. Suspension degradation under nonlinear damage law for good mode of road excitation.

Figure 38. Suspension RUL as a function of degradation for good mode of road excitation.

Figure 39. Degradation and CPP parameters for mode 3.

Figure 40. Degradation and CPP parameters with MChf for mode 3.

Figure 41. Degradation, rescaled RUL, and CPP parameters for mode 3.

Figure 42. Degradation, rescaled RUL, and CPP parameters with MChf for mode 3.

Figure 43. DOK and Chf in terms of N and of each other for mode 3.

Figure 44. P_r and P_m/i in terms of N and of each other for mode 3.

Figure 45. The complex probability vector Z in terms of N for mode 3.

Figure 46. Suspension degradation under nonlinear damage law for the three modes of road excitation.

Figure 47. Suspension RUL as a function of degradation for the three modes of road excitation.

Figure 48. Degradation and CPP parameters for the three modes.

Figure 49. Degradation and CPP parameters with MChf for the three modes.

Figure 50. Degradation, rescaled RUL, and CPP parameters for the three modes.

Figure 51. Degradation, rescaled RUL, and CPP parameters with MChf for the three modes.