Uncertainty Evaluation in the Design of Structural Health Monitoring Systems for Damage Detection†
Abstract
:1. Introduction
2. Materials and Methods
2.1. Numerical Modeling of SHM Signals
- Built a model of the reduced domain near the rivet hole in ANSYS (ANSYS® Mechanical APDL) with a sensing circle and non-reflecting boundary conditions.
- Evaluated the time-harmonic solutions to the wave scattering problem for frequencies of 2–1000 kHz at 2 kHz intervals, using the finite elements in ANSYS.
- Post-process FEM outputs generated complex scatter-cubes with wave-damage interaction coefficients (WDIC),
- Imported WDIC to Waveform Revealer 2-D (WFR-2D) in order to generate signal data analytically.
Finite Element Modeling
2.2. Experimental Factors and Damage Indices
2.3. Statistical Experimental Design and Analysis Methods
2.3.1. Full Factorial Design
2.3.2. Half-Fraction Factorial Design
3. Results
3.1. SHM Configuration Factors Producing the Most Variation in the SHM Response (Damage Index)
3.2. SHM Configuration Factors Identified through the Half-Fraction Factorial Design
4. Discussion
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Label | Factor | Generic Level | Specific Values |
---|---|---|---|
A | Transmitter Angle, θ | Low | 9° |
High | 27° | ||
B | Receiver Angle, φ | Low | 5° |
High | 20° | ||
C | Frequency | Low | 200 kHz |
High | 550 kHz | ||
D | Sensor Size | Low | 5 mm |
High | 7 mm | ||
E | Distance between Excitation and Damage Site | Low | 150 mm |
High | 250 mm | ||
F | Flaw Size | Low | 0.64 mm |
High | 3.20 mm |
Run | A | B | C | D | E | F |
---|---|---|---|---|---|---|
Transmitter Angle | Receiver Angle | Frequency | Sensor Size | Distance to Excitation | Flaw Size | |
1 | L | L | L | L | L | L |
2 | H | L | L | L | L | L |
3 | L | H | L | L | L | L |
4 | H | H | L | L | L | L |
... | ... | ... | ... | ... | ... | ... |
63 | H | H | H | H | H | L |
64 | H | H | H | H | H | H |
Factors for the Half-Fraction Factorial Design (and Associated Aliased Factor) | |||||
---|---|---|---|---|---|
A = BCDEF | AB = CDEF | BD = ACEF | DE = ABCF | ABC = DEF | ACF = BDE |
B = ACDEF | AC = BDEF | BE = ACDF | DF = ABCE | ABD = CEF | ADE = BCF |
C = ABDEF | AD = BCEF | BF = ACDE | EF = ABCD | ABE = CDF | ADF = BCE |
D = ABDEF | AE = BCDF | CD = ABEF | ABF = CDE | AEF = BCD | |
E = ABCDF | AF = BCDE | CE = ABDF | ACD = BEF | ||
F = ABCDE | BC = ADEF | CF = ABDE | ACE = BDF |
Factor | lnDIcc | lnsqdev | lndiffPA | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Sums of Squares | df | p-Value | Sums of Squares | df | p-Value | Sums of Squares | df | p-Value | |||
A | 1166.46 | 1 | <0.0001 | 1518.10 | 1 | <0.0001 | 164.57 | 1 | <0.0001 | ||
B | - | - | - | - | - | - | 12.18 | 1 | 0.0030 | ||
C | 21.81 | 1 | <0.0001 | 38.05 | 1 | <0.0001 | 3.22 | 1 | 0.1180 | ||
E | 10.68 | 1 | 0.0002 | 54.86 | 1 | <0.0001 | - | - | - | ||
AE | - | - | - | 10.85 | 1 | <0.0001 | - | - | - | ||
AC | - | - | - | 41.97 | 1 | <0.0001 | 23.58 | 1 | <0.0001 | ||
AB | - | - | - | - | - | - | 24.96 | 1 | <0.0001 | ||
BC | - | - | - | - | - | - | 0.14 | 1 | 0.7440 | ||
ABC | - | - | - | - | - | - | 24.01 | 1 | <0.0001 | ||
Error | 39.61 | 60 | 36.23 | 58 | 71.66 | 56 | |||||
Total | 1238.56 | 63 | 1700.07 | 63 | 324.25 | 63 | |||||
R2 | 0.9680 | 0.9787 | 0.7790 | ||||||||
RMSE | 0.8125 | 0.7903 | 1.1312 |
Factor | lnDIcc | lnsqdev | lndiffPA | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Sums of Squares | df | p-Value | Sums of Squares | df | p-Value | Sums of Squares | df | p-Value | |||
A | 608.68 | 1 | <0.0001 | 834.34 | 1 | <0.0001 | 117.51 | 1 | <0.0001 | ||
C | 14.80 | 1 | 0.0002 | 15.86 | 1 | 0.0016 | - | - | - | ||
E | 7.00 | 1 | 0.0065 | 23.45 | 1 | <0.0001 | - | - | - | ||
AE | - | - | - | 5.96 | 1 | 0.0039 | - | - | - | ||
AC | - | - | - | 6.37 | 1 | 0.0019 | - | - | - | ||
Error | 22.64 | 28 | 25.96 | 26 | 64.16 | 30 | |||||
Total | 653.12 | 31 | 911.93 | 31 | 181.67 | 31 | |||||
R2 | 0.9653 | 0.9736 | 0.6468 | ||||||||
RMSE | 0.8993 | 0.9992 | 1.4642 |
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Schubert Kabban, C.; Uber, R.; Lin, K.; Lin, B.; Bhuiyan, M.Y.; Giurgiutiu, V. Uncertainty Evaluation in the Design of Structural Health Monitoring Systems for Damage Detection†. Aerospace 2018, 5, 45. https://doi.org/10.3390/aerospace5020045
Schubert Kabban C, Uber R, Lin K, Lin B, Bhuiyan MY, Giurgiutiu V. Uncertainty Evaluation in the Design of Structural Health Monitoring Systems for Damage Detection†. Aerospace. 2018; 5(2):45. https://doi.org/10.3390/aerospace5020045
Chicago/Turabian StyleSchubert Kabban, Christine, Richard Uber, Kevin Lin, Bin Lin, Md Yeasin Bhuiyan, and Victor Giurgiutiu. 2018. "Uncertainty Evaluation in the Design of Structural Health Monitoring Systems for Damage Detection†" Aerospace 5, no. 2: 45. https://doi.org/10.3390/aerospace5020045