Nuclear Accident Emergency Response System: Radiation Field Estimation and Evacuation
Abstract
:1. Introduction
 1.
 Design a nuclear accident emergency response system consisting of radiation field estimation and evacuation. Based on UAV and bus collaboration, it can provide efficient, reliable and safe nuclear emergency response strategy for the decisionmaker;
 2.
 Analyze the optimal measurement coordinates considering the mobility of UAV. The CRLBbased coordinates optimization combined with UAV routing is formulated as an MINLP problem, and then solved by a twostage solution procedure;
 3.
 Improve the bus evacuation MILP model proposed by Bolia [16], in which both the evacuation time and the radiation exposure to evacuees are taken into consideration. The optimal evacuation route for buses can be directly obtained by commercial solvers.
2. Literature Review
3. UAVBased Nuclear Radiation Field Estimation
3.1. Radiation Measurement Model
3.2. CRLBBased Metric
3.3. Coordinates Optimization Problem Formulation
3.4. TwoStage Solution Procedure
Algorithm 1 Twostage solution procedure. 
Require:${Q}_{0}$; ${\pi}_{l}$; ${\pi}_{u}$; v; the initial model parameters $\widehat{\mathbf{\theta}}$; the initial UAV depots ${s}_{0}$ Ensure:${\pi}_{i}$; ${g}_{ik}$

Algorithm 2 UAVbased nuclear radiation field estimation. 
Require:${Q}_{0}$; ${\pi}_{l}$; ${\pi}_{u}$; v; $\widehat{\mathbf{\theta}}$; ${s}_{0}$; the time interval $\Delta t$ Ensure: The timevarying parameters of diffusion model

4. BusBased Nuclear Emergency Evacuation
4.1. Assumption and Description
 1.
 People arrive at the nearest pickup point in advance to wait for evacuation, and the transfer time and radiation exposure are ignored;
 2.
 The loading and unloading time of buses for pickup points and shelters are ignored;
 3.
 The capacities of buses at different depots and the demands of different pickup points are known;
 4.
 The locations of the depots, pickup points, and shelters are known and the travel time between them are constant;
 5.
 Each pickup point has a particular shelter, i.e., a bus only takes evacuees from a pickup point to the assigned shelter during one trip, even if not fully loaded;
 6.
 The shelter can accommodate all evacuees from the corresponding pickup points;
 7.
 The radiation dose per second of each route and each pickup point are constant and known during one trip.
4.2. Mathematical Formulation
5. Simulation Results
 1.
 More information can be obtained from more measurements, resulting in smaller parameter RMS error;
 2.
 Based on the optimal measurement coordinates, even smaller parameter RMS error can be achieved with fewer measurements.
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
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UAVs  x (m)  y (m)  z (m)  t (s) 

1  173.027  244.802  26.545  608.697 
300.989  184.739  121.332  616.847  
303.188  180.700  125.570  618.166  
318.715  174.929  120.500  619.946  
2  −109.613  −141.109  49.005  613.547 
−65.560  −156.113  63.143  616.615  
−39.174  −159.356  69.787  618.815  
−41.453  −158.657  70.184  619.958  
3  299.851  247.711  4.064  615.587 
256.180  284.296  56.412  619.909 
Instance  Depots  Pickups  Shelters  Buses  Capacity 

1  1  5  2  20  25 
2  1  5  2  25  20 
3  2  10  3  8, 12  25 
4  2  10  3  5, 10  25, 30 
5  2  10  3  10, 10  25, 30 
Instance  Gap  Compt Time (t)  Evac Time (t)  Radiation 

1  0%  22.77  611.48  $1.36\times {10}^{7}$ 
2  0%  35.80  611.48  $1.33\times {10}^{7}$ 
3  0%  144.98  453.32  $1.63\times {10}^{7}$ 
4  0%  231.73  473.42  $1.55\times {10}^{7}$ 
5  0.65%  time limit  449.09  $1.53\times {10}^{7}$ 
Bus  Trips  Evac Time  

1  2  3  4  
1  8  9  10  4  373.82 
2  9  9  10  5  351.21 
3  8  10  10  5  355.96 
4  8  10  10  5  355.96 
5  9  9  10  5  351.37 
6  2  2  4  5  473.42 
7  3  1  4  5  472.14 
8  3  99.22  
9  7  6  6  5  465.18 
10  7  6  6  5  465.18 
11  8  9  8  5  441.09 
12  2  1  3  3  449.09 
13  7  6  6  4  469.59 
14  3  99.22  
15  7  6  6  5  465.18 
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Chen, B.; Li, Z.; Yang, Z. Nuclear Accident Emergency Response System: Radiation Field Estimation and Evacuation. Sustainability 2022, 14, 5663. https://doi.org/10.3390/su14095663
Chen B, Li Z, Yang Z. Nuclear Accident Emergency Response System: Radiation Field Estimation and Evacuation. Sustainability. 2022; 14(9):5663. https://doi.org/10.3390/su14095663
Chicago/Turabian StyleChen, Bo, Zhicheng Li, and Zaiyue Yang. 2022. "Nuclear Accident Emergency Response System: Radiation Field Estimation and Evacuation" Sustainability 14, no. 9: 5663. https://doi.org/10.3390/su14095663