Categorization of the Condition of Railway Embankments Using a Multi-Attribute Utility Theory
Abstract
:1. Introduction
2. Methodology
2.1. The Multi-Attribute Utility Theory (MAUT)
2.2. Selection of Attributes
2.2.1. Attribute 1: Maintenance History
2.2.2. Attribute 2: Visual Assessment of External Irregularities
- Observable embankment slope slips (material failure in the side slope);
- Observable embankment bulging (evidence of the slide slopes expanding laterally);
- Observable crest settlement (suggesting settlement of the material beneath the embankment);
- Broken sleepers.
2.2.3. Attributes 3–5: A GPR Investigation Data
Attribute 3: The Depth of Ballast Layer (Ballast Pockets)
Attribute 4: Ballast Fouling (Quality of Ballast Layer)
Attribute 5: Irregularities in Sub-Ballast and Embankment Fill
2.3. Implementation of Multi-Attribute Utility Theory
- —normalized utility function value for Attribute i and Alternative j
- Sj—Alternative j, subsection of 100 m in length; j = 1, 2, …, m
- m—number of alternatives
- QVC,i—quantification value of Attribute i; i = 1, 2, …, n
- n—number of attributes
- wi—weight of importance for Attribute i
- —the overall utility function value for Alternative j
3. Case Study Example
3.1. Description of the Case Study Area
3.2. Data Acquisition Procedure
3.3. Results and Discussion
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Trace Number | Investigation Distance (m) | Measured Depth (m) | Average Measured Depth (m) | ||
---|---|---|---|---|---|
1 (1st overall) | 0.0 | dmeasured,0 | − 0.5 m | ||
2 (21st overall) | 1.0 | dmeasured,1 | |||
3 (41st overall) | 2.0 | dmeasured,2 | |||
… | … | … | |||
100 (2001st overall) | 100.0 | dmeasured,100 |
Trace Number | Investig. Distance (m) | Average Amplitude Decrease AAD (−) | Signal Attenuation, i.e., Ballast Fouling (BQ) (−) | BQ Average × 100 (%) | |
---|---|---|---|---|---|
1 (1st overall) | 0.0 | AADn = | (BQ)1 = 1 − | ||
1 (2nd overall) | 0.05 | AADn+1 = | (BQ)2 = 1 − | ||
2 (3rd overall) | 0.10 | AADn+2 = | (BQ)3 = 1 − | ||
3 (4th overall) | 0.15 | AADn+3 = | (BQ)4 = 1 − | ||
… | … | … | … | ||
2001 (2001st overall) | 100.0 | AAD2001 = | (BQ)2001 = 1 − |
Attribute QV (n) | QVC1 | QVC2 | QVC3 | QVC4 | QVC5 | |
---|---|---|---|---|---|---|
Alternatives (m) | ||||||
S1 | ||||||
S2 | ||||||
… | … | … | … | … | … | |
Sm |
Category | Condition | Graphical Representation | MAUT Condition |
---|---|---|---|
1 | Very poor | ||
2 | Poor | ||
3 | Adequate | ||
4 | Good | ||
5 | Very good |
Attribute | Alternative | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|---|
km 0.0–0.1 | km 0.1–0.2 | km 0.2–0.3 | km 0.3–0.4 | km 0.4–0.5 | km 0.5–0.6 | km 0.6–0.7 | km 0.7–0.8 | km 0.8–0.9 | km 0.9–1.0 | ||
Tampering per year | 3 | 0 | 0 | 5 | 2 | 3 | 3 | 4 | 2 | 2 | |
QVC1 | 0.60 | 0.00 | 0.00 | 1.00 (QSVC1) | 0.40 | 0.60 | 0.60 | 0.80 | 0.40 | 0.40 | |
% of visual irregularities per section | 10 | 0 | 5 | 70 | 90 | 40 | 40 | 50 | 50 | 40 | |
QVC2 | 0.11 | 0.00 | 0.56 | 0.77 | 1.00 (QSVC2) | 0.44 | 0.44 | 0.56 | 0.56 | 0.44 | |
average depth (m) | 1.32 | 1.25 | 1.29 | 1.34 | 1.36 | 1.17 | 1.23 | 1.09 | 1.05 | 1.06 | |
QVC3 | 0.95 | 0.87 | 0.92 | 0.98 | 1.00 (QSVC3) | 0.78 | 0.84 | 0.69 | 0.64 | 0.65 | |
fouled % per section | 40 | 10 | 50 | 80 | 60 | 20 | 20 | 30 | 30 | 40 | |
QVC4 | 0.50 | 0.13 | 0.63 | 1.00 (QSVC4) | 0.75 | 0.25 | 0.25 | 0.38 | 0.38 | 0.50 | |
GPR irregularities per section | 0 | 1 | 2 | 4 | 0 | 0 | 2 | 4 | 0 | 0 | |
QVC5 | 0.00 | 0.25 | 0.50 | 1.00 (QSVC5) | 0.00 | 0.00 | 0.50 | 1.00 (QSVC5) | 0.00 | 0.00 |
Attribute | Label | Mean | SD | Calculated Weight of Importance (w) |
---|---|---|---|---|
Supervision Center Information | QVC1 | 9.30 | 0.78 | 0.243 |
Visual Assessment | QVC2 | 5.60 | 1.19 | 0.146 |
Ballast depth (ballast pockets) | QVC3 | 8.40 | 0.91 | 0.219 |
Ballast fouling (ballast quality) | QVC4 | 8.70 | 0.94 | 0.227 |
Irregularities in sub-ballast and embankment fill | QVC5 | 6.30 | 1.21 | 0.164 |
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Kovačević, M.S.; Bačić, M.; Stipanović, I.; Gavin, K. Categorization of the Condition of Railway Embankments Using a Multi-Attribute Utility Theory. Appl. Sci. 2019, 9, 5089. https://doi.org/10.3390/app9235089
Kovačević MS, Bačić M, Stipanović I, Gavin K. Categorization of the Condition of Railway Embankments Using a Multi-Attribute Utility Theory. Applied Sciences. 2019; 9(23):5089. https://doi.org/10.3390/app9235089
Chicago/Turabian StyleKovačević, Meho Saša, Mario Bačić, Irina Stipanović, and Kenneth Gavin. 2019. "Categorization of the Condition of Railway Embankments Using a Multi-Attribute Utility Theory" Applied Sciences 9, no. 23: 5089. https://doi.org/10.3390/app9235089
APA StyleKovačević, M. S., Bačić, M., Stipanović, I., & Gavin, K. (2019). Categorization of the Condition of Railway Embankments Using a Multi-Attribute Utility Theory. Applied Sciences, 9(23), 5089. https://doi.org/10.3390/app9235089