Weighted Regression-Based Extremum Response Surface Method for Structural Dynamic Fuzzy Reliability Analysis
Abstract
:1. Introduction
2. Basic Theory on Dynamic Fuzzy Reliability Analysis
2.1. Weighted Regression Extremum Response Surface Method (WR-ERSM) Modeling
2.2. Safety Criterion Transformation
2.3. Structural Dynamic Fuzzy Reliability Analysis
3. Example Analysis
3.1. Deterministic Analysis for Turbine Blisk
3.2. The WR-ERSM Model of Turbine Blisk
3.3. Turbine Blisk Reliability Evaluation
4. WR-ERSM Verification Procedure
4.1. Model-Fitting Properties
4.2. Simulation Performances for Dynamic Fuzzy Reliability Analysis of Turbine Blisk
5. Conclusions
- (1)
- The WR-ERSM is highly precise and efficient in structural dynamic reliability evaluation, since ERSM has the capacity of processing the transient problem;
- (2)
- The WR approach can improve modeling accuracy so that the proposed WR-ERSM possesses high fitting efficiency and accuracy, due to the requirement of small samples;
- (3)
- WR-ERSM possesses good simulation performance in structural dynamic fuzzy reliability evaluation, as the fuzzy safety criterion is considered to improve the precision;
- (4)
- The change rule of turbine blisk structural stress from start to cruise for an aircraft is acquired with the maximum value of structural stress at t = 165 s and the reliability degree (Pr = 0.997) of the turbine blisk.
- (5)
- The efforts of this study provide a promising method for the dynamic reliability analysis and evaluation of complex structures with respect to the working process.
Author Contributions
Funding
Conflicts of Interest
References
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Parameters | Variable | Distribution | Mean, μ | St.Dev., δ |
---|---|---|---|---|
Inlet velocity (m·s−1) | v | Normal | 168 | 5.04 |
Inlet pressure (Pa) | P | Normal | 600,000 | 12,000 |
Material density (kg·m−3) | ρ | Normal | 8210 | 246 |
Angular speed (rad·s−1) | w | Normal | 1168 | 35 |
Parameters and Weighted Coefficient | Parameters and Weighted Coefficient | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
v m·s−1 | P, ×105 Pa | ρ kg·m−3 | w rad·s−1 | σ × 108 Pa | W | v, m·s−1 | P, ×105 Pa | ρ, kg·m−3 | w, rad·s−1 | σ, ×108 Pa | W |
168.00 | 6.00 | 8210 | 1168 | 9.687 | 0.9105 | 173.04 | 6.00 | 8210 | 1133 | 9.098 | 0.9694 |
162.96 | 6.00 | 8210 | 1168 | 9.693 | 0.9099 | 168.00 | 6.12 | 8210 | 1133 | 9.105 | 0.9687 |
168.00 | 5.88 | 8210 | 1168 | 9.686 | 0.9106 | 168.00 | 6.00 | 7964 | 1133 | 8.827 | 0.9992 |
168.00 | 6.00 | 7964 | 1168 | 9.392 | 0.9391 | 173.04 | 5.88 | 7964 | 1168 | 9.385 | 0.9398 |
168.00 | 6.00 | 8210 | 1133 | 9.105 | 0.9687 | 173.04 | 5.88 | 8210 | 1133 | 9.098 | 0.9694 |
173.04 | 6.00 | 8210 | 1168 | 9.686 | 0.9391 | 162.96 | 6.12 | 7964 | 1168 | 9.398 | 0.9385 |
168.00 | 6.12 | 8210 | 1168 | 9.687 | 0.9105 | 162.96 | 6.12 | 8210 | 1133 | 9.111 | 0.9681 |
168.00 | 6.12 | 8210 | 1203 | 10.29 | 0.8576 | 168.00 | 6.00 | 8456 | 1203 | 10.59 | 0.8575 |
162.96 | 5.88 | 8210 | 1168 | 9.687 | 0.9105 | 168.00 | 6.12 | 7964 | 1133 | 8.829 | 0.9989 |
162.96 | 6.00 | 7964 | 1168 | 9.391 | 0.9392 | 162.96 | 6.00 | 8456 | 1133 | 9.389 | 0.9394 |
162.96 | 6.00 | 8210 | 1133 | 9.105 | 0.9687 | 168.00 | 5.88 | 8456 | 1133 | 9.383 | 0.9400 |
168.00 | 5.88 | 7964 | 1168 | 9.391 | 0.9392 | 173.04 | 6.12 | 7964 | 1168 | 9.385 | 0.9398 |
168.00 | 5.88 | 8210 | 1133 | 9.105 | 0.9687 | 173.04 | 6.12 | 8210 | 1133 | 9.098 | 0.9694 |
168.00 | 6.00 | 7964 | 1133 | 8.827 | 0.9992 | 173.04 | 6.00 | 8456 | 1133 | 9.376 | 0.9407 |
173.04 | 6.12 | 8210 | 1168 | 9.687 | 0.9105 | 168.00 | 6.12 | 8456 | 1133 | 9.383 | 0.9400 |
162.96 | 6.12 | 8210 | 1168 | 9.693 | 0.9099 | 162.96 | 5.88 | 7964 | 1168 | 9.398 | 0.9385 |
168.00 | 6.00 | 8210 | 1203 | 10.28 | 0.8576 | 173.04 | 6.00 | 8210 | 1203 | 10.28 | 0.8576 |
173.04 | 5.88 | 8210 | 1168 | 9.681 | 0.9111 | 162.96 | 5.88 | 8210 | 1133 | 9.111 | 0.9681 |
173.04 | 6.00 | 7964 | 1168 | 9.385 | 0.9398 | 162.96 | 6.00 | 7964 | 1133 | 8.827 | 0.9992 |
168.00 | 6.12 | 7964 | 1168 | 9.391 | 0.9392 | 168.00 | 5.88 | 7964 | 1133 | 8.826 | 0.9993 |
Method | Fitting ERSM Model | Fitting Accuracy | ||
---|---|---|---|---|
Sample Number | Fitting Time, h | r2 | rmax | |
WR-ERSM | 9 | 7.05 | 0.9984 | 0.0535 |
ERSM | 29 | 22.39 | 0.9742 | 0.0834 |
Methods | Pr | Errors | Precision, % |
---|---|---|---|
MC method | 0.9981 | - | - |
ESTM | 0.9962 | 0.0019 | 99.81 |
ERSM | 0.9937 | 0.0044 | 99.56 |
WR-ERSM | 0.9970 | 0.0011 | 99.89 |
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Lu, C.; Feng, Y.-W.; Fei, C.-W. Weighted Regression-Based Extremum Response Surface Method for Structural Dynamic Fuzzy Reliability Analysis. Energies 2019, 12, 1588. https://doi.org/10.3390/en12091588
Lu C, Feng Y-W, Fei C-W. Weighted Regression-Based Extremum Response Surface Method for Structural Dynamic Fuzzy Reliability Analysis. Energies. 2019; 12(9):1588. https://doi.org/10.3390/en12091588
Chicago/Turabian StyleLu, Cheng, Yun-Wen Feng, and Cheng-Wei Fei. 2019. "Weighted Regression-Based Extremum Response Surface Method for Structural Dynamic Fuzzy Reliability Analysis" Energies 12, no. 9: 1588. https://doi.org/10.3390/en12091588