An Efficient Framework for Multi-Objective Risk-Informed Decision Support Systems for Drainage Rehabilitation
Abstract
:1. Introduction
2. Materials and Methods
2.1. Introduction to the Hydraulics and Risk Combined Model Model
2.2. Algorithm Frameworks
HRCM Model Simulation Frameworks
2.3. Revised HRCM Method (RHRCM)
2.4. Case Study
2.5. Model Performance Evaluation
Sensitivity Analysis
3. Results
3.1. Computational Time Competition
3.2. Methods Evaluation
3.2.1. Scenario 1—Narrow Pipe
3.2.2. Scenario 2—Ageing Pipe
4. Discussion
4.1. Advantage and Limitation of RHRCM Method
4.2. Discrete Versus Continuous Data
4.3. Parallel Results Problem
4.4. Framework
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Rehabilitation Number | Action | Rehabilitation Cost ($/m) | Disruption Cost ($/m) | Pipe Cost ($/m) | Benefit (Year) |
---|---|---|---|---|---|
1 | Do nothing | 0 | 0 | 0 | - |
2 | Routine cleaning | 16 | 0 | 0 | 10 |
3 | Shotcrete | 656 | 0 | 0 | 20 |
4 | Cured-in-place pipe | 1558 | 0 | 0 | 50 |
5 | Reinforced fiberglass sliplining | 2231 | 0 | 0 | 100 |
6 | Dig and replace with concrete pipe | 1148 | 656 | 1 | 50 |
Name | Discrete Pipe | Constraint Functions 1 | Diagnostic Model 2 | Network Index 3 | Objective Cost | GA |
---|---|---|---|---|---|---|
GA-HRCM | √ | √ | √ | √ | ||
GA-Continuous | √ | √ | √ | |||
GA-Cost | √ | √ | √ | √ | √ | |
GA-Unconstrainted | √ | √ | √ | |||
GA-Network | √ | √ | √ | √ | ||
PSO-HRCM | √ | √ | ||||
PSO-Cost | √ | √ | √ | |||
RHRCM | √ | √ | √ |
Classification | Scenario | Description | Function |
---|---|---|---|
Hydraulic | 1 | A system with one narrow pipe (poor hydraulic performance) at the chain route. The diameter of pipe (C8) is replaced to 0.1 m. The age of all the pipes is zero. | In this simulation, it was tested whether the method can detect the narrow pipe. |
Ageing risk | 2 | A system with a pipe at high risk but there is no hydraulic risk. The diameters of pipes are presented in Figure 4b. The age of pipe C9 was 60, and other pipes ages are zero. | In this simulation, it was tested whether the method can detect an aged pipe. |
Method | Convergent Population | Convergent Time (s) | 2500 Time (s) | 2500 Number of Solutions | 2500 Average Cost (million $) | 2500 Cost Effectiveness | |
---|---|---|---|---|---|---|---|
Hydro 1 | Risk 2 | ||||||
GA-HRCM | 2000 | 182,334 | 372,035 | 6 | 0.67 | 54.81 | 31.36 |
GA-Continuous | 1500 | 116,374 | 232,122 | 5 | 0.44 | 62.65 | 33.60 |
GA-Cost | N/A | N/A | 298,599 | 34 | 0.30 | 138.26 | 73.92 |
GA-Network | 500 | 36696 | 229,006 | 4 | 0.70 | 43.97 | 23.82 |
GA-Unconstraint | N/A | N/A | 84,157 | 8 | 0.78 | 47.81 | 24.64 |
PSO-HRCM | N/A | N/A | 223,591 | 5 | 1.03 | 28.16 | 13.99 |
PSO-Cost | N/A | N/A | 268,340 | 13 | 0.61 | 45.24 | 22.18 |
RHRCM | N/A | N/A | 89,182 | 10 | 0.30 | 177.29 | 87.82 |
Method | Convergent Population | Convergent Time (s) | 2500 Time (s) | 2500 Number of Solutions | 2500 Average Cost (million$) | 2500 Cost Effectiveness | |
---|---|---|---|---|---|---|---|
Hydro 1 | Risk 2 | ||||||
GA-HRCM | N/A | N/A | 163,519 | 6 | 0.65 | 4.46 | 40.77 |
GA-Continuous | 1500 | 232,415 | 222,536 | 6 | 0.67 | 3.64 | 39.66 |
GA-Cost | N/A | N/A | 277,206 | 40 | 0.24 | 13.92 | 129.50 |
GA-Network | N/A | N/A | 196,281 | 6 | 0.66 | 3.69 | 41.07 |
GA-Unconstraint | 2000 | 86,322 | 406,361 | 6 | 0.73 | 4.40 | 36.62 |
PSO-HRCM | N/A | N/A | 219,888 | 5 | 1.00 | 3.30 | 19.87 |
PSO-Cost | N/A | N/A | 309,305 | 33 | 0.63 | 4.29 | 27.17 |
RHRCM | N/A | N/A | 89,863 | 30 | 0.26 | 11.70 | 137.31 |
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Cai, X.; Mohammadian, A.; Shirkhani, H. An Efficient Framework for Multi-Objective Risk-Informed Decision Support Systems for Drainage Rehabilitation. Math. Comput. Appl. 2020, 25, 73. https://doi.org/10.3390/mca25040073
Cai X, Mohammadian A, Shirkhani H. An Efficient Framework for Multi-Objective Risk-Informed Decision Support Systems for Drainage Rehabilitation. Mathematical and Computational Applications. 2020; 25(4):73. https://doi.org/10.3390/mca25040073
Chicago/Turabian StyleCai, Xiatong, Abdolmajid Mohammadian, and Hamidreza Shirkhani. 2020. "An Efficient Framework for Multi-Objective Risk-Informed Decision Support Systems for Drainage Rehabilitation" Mathematical and Computational Applications 25, no. 4: 73. https://doi.org/10.3390/mca25040073