Aviation emergency rescue is an effective means of nature disaster relief that is widely used in many countries. The dispatching plan of aviation emergency rescue guarantees the efficient implementation of this relief measure. The conventional dispatching plan that does not consider random wind factors leads to a nonprecise quick-responsive scheme and serious safety issues. In this study, an aviation emergency rescue framework that considers the influence of random wind at flight trajectory is proposed. In this framework, the predicted wind information for a disaster area is updated by using unscented Kalman filtering technology. Then, considering the practical scheduling problem of aircraft emergency rescue at present, a multiobjective model is established in this study. An optimization model aimed at maximizing the relief supply satisfaction, rescue priority satisfaction, and minimizing total rescue flight distance is formulated. Finally, the transport times of aircraft with and without the influence of random wind are analyzed on the basis of the data of an earthquake disaster area. Results show that the proposed dispatching plan that considers the constraints of updated wind speed and direction is highly applicable in real operations.
Among all countermeasures for disaster relief and emergency response treatment, air rescue is the most effective and popular one globally; this approach offers the advantages of high speed, high efficiency, and few geospatial constraints [
Static emergency resource scheduling is the primary issue of optimizing a combination of rescue points. However, in practice, resource scheduling is often conducted in multiple stages because of inadequate information. The resource amount scheduled at a certain stage is closely linked to the resource amount scheduled at the prior stage. Therefore, the dynamic resource scheduling model [
Meanwhile, the demand difference of various types of emergency goods and the fuel consumption of aircraft can lead to divergent scheduling decisions. Moreover, the conventional dispatching plan [
The rest of the paper is organized as follows. In Section
UKF is an algorithm that combines unscented transformation and Kalman filtering [
Assuming that
After the
Three parameters, namely,
The values of wind speed and direction with respect to the time series can be regarded as the discrete nonlinear system as follows:
Assuming that the process noise
In (
In this subsection, an airplane motion model was built. The synthesis of random wind speed and true airplane airspeed is described in Figure
Normal composite of random wind speed and true airplane speed.
By analyzing the historical random wind data from the international ground exchange station, we assumed that the wind speed components
The scheduling problem in this study refers to the reasonable arrangement of flight routes of aircraft in a supply-demand relation system. This system involves several aircraft, rescue points, and devastated points. The main aim is to achieve the optimal values of different objective functions while meeting the constraints (e.g., maximum payload constraint of the aircraft, maximum flight radius constraint of the aircraft, and material demand constraint). The objective functions are as follows:
Supplies are the object of transportation. Relief supplies of every devastated point or rescue point can be viewed as a consignment of goods. Such goods feature different types of attributes (e.g., fast-moving consumer goods or durable goods), weight and volume, required arrival time and devastated point, and permission of partial distribution. Weight of supplies is the basis of decision making on aircraft load. If the demand for supplies of one devastated point exceeds the maximum payload of the aircraft, then rearranging another aircraft is necessary. The rescue priority of devastated points and the distance between rescue points are the basis of flight route planning for aircraft.
It is the carrier of relief supplies, and its main attributes include type, maximum fuel load, fuel consumption per hour, average flight speed, maximum climb rate, ceiling, and maximum payload. Aircraft participating in rescue mainly includes different models of helicopters of General Aviation and some large-load transport planes. In this study, M-171, M-8, Y7-100, and Y5-B(K) are chosen as the rescuing aircrafts. The maximum payload of aircraft refers to the maximum loading weight of the aircraft. It is the primary constraint of aircraft performance and an important reference for scheduling decision making. Aircraft must return to the starting point after the delivery of supplies.
It is the place supplied with the relief goods and the command central hub of aircraft. A distribution scheduling task can involve one or several central hubs, and the offered relief supplies can be a single variety or diversified. The total material storage can meet all or the partial demands for supplies of all devastated points.
Its attributes include material demands, rescue priority, and material satisfaction. In a distribution system, the material demands of one devastated point can be larger or smaller than the maximum payload of one aircraft. Rescue priority is divided according to the actual disaster conditions of devastated points and is integral within a certain range. Relief supply satisfaction includes full satisfaction and partial satisfaction.
It is composed of vertexes (rescue points and devastated points) and directed arc. The attributes of sides and arcs include direction, weight, material distribution quantity, and traffic flow limit. Weight can be expressed in time, cost, or distance. This attribute can also either change with time or type of aircraft or remain constant. The traffic flow of vertexes, sides, and arcs in the transport network can be considered as infinite flow, such as the quantity of aircraft loading or unloading in the same rescue point and flying in the same sides and arcs.
Aircrafts influenced by random winds deviate from the planned route. To ensure that the aircraft follows the planned route, the track angle should be equivalent to the course angle and thus offset the bias caused by crosswind. When several rescue points are available for different groups of devastated points, locations of rescue points and devastated points are fixed. In addition, different types of relief supplies in the rescue points can meet the material demands of devastated points. The mixing of material loadings of different devastated points is allowed. In other words, relief supplies for different devastated points can be loaded onto the same aircraft. The relief supplies of every devastated point should be satisfied at the lowest extent and be distributed by one aircraft. No partial shipment is allowed. The material loads of every aircraft should not exceed its maximum payload. Given that the maximum fuel load of aircraft is fixed, the maximum flight distance of every aircraft should not exceed its maximum flight radius. During material distribution, every aircraft should take off from the rescue point and return to the rescue point after delivering relief supplies to the devastated points in the area under administration. The time interval in this study is extremely short. Therefore, relief supplies of rescue points and the material demands of devastated points are kept the same in the defined period. Aircraft can only be refueled and loaded in rescue points, and they can only release or unload supplies at devastated points.
In this subsection, the model variables are provided in Notations.
For every devastated point group, the objective functions of maximum relief supply satisfaction
Constraint (
In this study, the proposed model and the emergency logistics distribution model in [
Get the preliminary information of the disaster area, and determine the relief supplies of rescue points, disaster relief priorities, and supplies demand of devastated points.
According to the distance
Take one of the group, and make an initial planning for the aircrafts and materials within the group to meet the objectives which include the shortest total mileage of aircrafts, maximum rescue priority satisfaction, and maximum relief supply satisfaction.
Obtain aircraft flight performance, and estimate whether the actual flight mileage of all aircraft
Adopting aircraft flight performance, estimate whether the total distribution amount of all rescue aircraft
According to the amount of material supply and demand in Step
Through the above steps, we can complete the allocation of resources and path planning in any group. Then we repeat the operation of Steps
Following the above seven steps and combining with the rescue scene, we can get an optimal solution, which meets three objective functions and all constraints. However, we could not meet all the model optimal solution in many practical rescue. Therefore, we should take the suboptimal solution of the model into consideration. First of all, one or more feasible path of the rescue can be gotten when we meet the maximum target priority satisfaction. Secondly, when we meet the greatest satisfaction of material distribution and do not meet the maximum relief supply satisfaction, we can find the shortest path of total flight mileage in the rescue. So we could take second shortest path, or we find the result which meet shortest total mileage and do not meet maximum relief supply satisfaction. These possible solutions are called suboptimal solutions. In short, we can find the solution of three objective functions successively to get the relative optimal solution in the second-best solution.
The feasibility and validity of the proposed model were verified with the seismic data based on Wenchuan earthquake in Sichuan Province of China. The supply of rescue points and demands as well as the rescue priority of devastated points were determined according to actual disaster conditions in different regions. The parameters are listed in Tables
Supply of rescue points.
Number | Name | Supply/(kg) | |
---|---|---|---|
| | ||
1 | Chengdu Shuangliu Airport | 6000 | 4000 |
2 | Yibin Airport | 6000 | 4000 |
3 | Guangyuan Panlong Airport | 6000 | 4000 |
Demands of devastated points.
Number | Name | Rescue priority | Demands /(kg) | Minimum demands /(kg) | ||
---|---|---|---|---|---|---|
| | | | |||
4 | Hongbai Town | 4 | 1400 | 800 | 1000 | 500 |
5 | Qiandi Town | 5 | 1700 | 1100 | 1200 | 600 |
6 | Luoshui Town | 4 | 900 | 700 | 600 | 400 |
7 | Mazu Town | 2 | 600 | 500 | 300 | 300 |
8 | Louqiao Town | 1 | 800 | 500 | 600 | 300 |
9 | Qiaozhuang Town | 3 | 1100 | 900 | 800 | 600 |
10 | Qingxi Town | 3 | 1100 | 900 | 700 | 700 |
11 | Quhe Town | 4 | 1600 | 800 | 1300 | 500 |
12 | Shazhou Town | 1 | 400 | 300 | 300 | 200 |
13 | Suhe Town | 5 | 900 | 600 | 600 | 400 |
14 | Wali Town | 1 | 400 | 400 | 200 | 300 |
15 | Yaodu Town | 3 | 1300 | 800 | 800 | 600 |
16 | Sanguo Town | 2 | 900 | 600 | 600 | 400 |
17 | Yuexi Town | 4 | 1300 | 1000 | 1000 | 600 |
18 | Kangding Town | 2 | 1200 | 700 | 900 | 500 |
19 | Yongshan Town | 2 | 1300 | 1100 | 1000 | 800 |
20 | Ludian Town | 2 | 1100 | 600 | 700 | 300 |
21 | Jinggu Town | 4 | 700 | 700 | 500 | 400 |
In this study, four models of rescue aircraft were used: M-171, M-8, Y7-100, and Y5-B(K).
The performance parameters of the different aircraft models are listed in Table
Performance parameters of aircraft models.
Type | Maximum amount of fuel/(kg) | Average fuel consumption rate/(kg) | Average speed/(km/h) | Maximum payload/(kg) | Maximum climb rate/(m/s) | Ceiling/(m) |
---|---|---|---|---|---|---|
M171 | 2732 | 420 | 230 | 4000 | 9.3 | 10675 |
M8 | 2027 | 310 | 180 | 2900 | 7.7 | 6520 |
Y7-100 | 4790 | 690 | 423 | 5500 | 7.6 | 8750 |
Y5-B(K) | 900 | 250 | 190 | 1500 | 8.3 | 4500 |
The forecasted random wind data at the coordinates of the switching station were calculated with the hexahedral interpolation model [
Forecasted wind vector value at the switching station.
Number | Component | Component | Wind |
---|---|---|---|
direction | |||
1 | | 3.096002 | 178.7894 |
2 | | 3.074244 | 178.7762 |
3 | | 3.026139 | 178.7645 |
4 | | 2.927397 | 178.7533 |
5 | | 2.760375 | 178.7417 |
6 | | 2.726115 | 178.8577 |
7 | | 2.646679 | 178.8342 |
8 | | 2.53235 | 178.8083 |
9 | | 2.377908 | 178.7805 |
10 | | 2.184142 | 178.7516 |
11 | | 4.476649 | 178.9061 |
12 | | 4.410188 | 178.8829 |
13 | | 4.293882 | 178.8583 |
14 | | 4.110244 | 178.8331 |
15 | | 3.849385 | 178.8082 |
16 | | 5.754836 | 179.0035 |
17 | | 5.625553 | 178.9774 |
18 | | 5.451726 | 178.9529 |
19 | | 5.202419 | 178.9299 |
20 | | 4.854606 | 178.9076 |
21 | | 7.033259 | 179.1049 |
22 | | 6.957304 | 179.0834 |
23 | | 6.821929 | 179.0632 |
24 | | 6.588525 | 179.0439 |
25 | | 6.227895 | 179.0253 |
26 | | 4.129391 | 178.8669 |
27 | | 4.06918 | 178.8574 |
28 | | 3.996232 | 178.8485 |
29 | | 3.901841 | 178.8408 |
30 | | 3.778968 | 178.8349 |
31 | | 5.024794 | 178.8489 |
32 | | 5.091888 | 178.8448 |
33 | | 5.108503 | 178.8390 |
34 | | 5.049638 | 178.8321 |
35 | | 4.894799 | 178.8249 |
36 | | 4.09711 | 178.8203 |
37 | | 4.127017 | 178.8193 |
38 | | 4.106525 | 178.8176 |
39 | | 4.007229 | 178.8149 |
40 | | 3.810378 | 178.8113 |
Random wind component chart.
Resultant random wind velocity chart.
The proposed model was solved using Lingo. The aircraft scheduling results and distribution routes are shown in Table
Decision on aircraft emergency scheduling plan calculated by Lingo.
Devastated point in the group | Type | Route | Mileage/(km) | Total mileage/(km) | |
---|---|---|---|---|---|
Rescue point 1 | 4, 5, 6, 7, 8, 9 | Y7-100 | 1-5-4-1 | 646.5 | 1870.9 |
M-171 | 1-9-8-1 | 697.0 | |||
M-8 | 1-6-7-1 | 527.4 | |||
Rescue point 2 | 10, 11, 12, 13, 16, 17 | Y5-B(K) | 2-13-2 | 164.4 | 2448.2 |
M-171 | 2-17-16-2 | 772.4 | |||
M-8(two) | 2-10-12-2 | 626.5 | |||
2-11-2 | 884.9 | ||||
Rescue point 3 | 14, 15, 18, 19, 20, 21 | Y7-100 | 3-19-18-14-3 | 778.9 | 1901.7 |
Y5-B(K) | 3-21-3 | 544.4 | |||
M-171 | 3-15-20-3 | 578.4 |
Relief supply allocation calculated by Lingo.
Rescue point | Devastated point | | | Relief supply satisfaction |
---|---|---|---|---|
Area 1 | Area 4 | 1400 | 800 | 93.80% |
Area 5 | 1200 | 600 | ||
Area 6 | 900 | 700 | ||
Area 7 | 600 | 500 | ||
Area 8 | 800 | 500 | ||
Area 9 | 1100 | 900 | ||
Area 2 | Area 10 | 1100 | 1000 | 94.10% |
Area 11 | 1400 | 500 | ||
Area 12 | 400 | 300 | ||
Area 13 | 900 | 600 | ||
Area 16 | 900 | 600 | ||
Area 17 | 1300 | 1000 | ||
Area 3 | Area 14 | 400 | 400 | 97.70% |
Area 15 | 1300 | 800 | ||
Area 18 | 1200 | 700 | ||
Area 19 | 1300 | 800 | ||
Area 20 | 1100 | 600 | ||
Area 21 | 700 | 700 |
As shown in Tables
Decision on emergency aircraft scheduling plan for Wenchuan earthquake disaster region calculated by Lingo.
According to the optimal solutions calculated by Lingo, the routes of rescue point 2 change when the same grouping of devastated points and application of aircraft was applied. For example, the route of Y5-B(K) changes from 2-13-2 to 2-13-12-2, causing 168.4 km additional mileage of transport. The route of M-171 changes from 2-17-16-2 to 2-10-16-2, thereby increasing the mileage of transport by 118.8 km. The route of M-8 becomes 2-17-2 and 2-11-2 rather than 2-10-12-2 and 2-1-2, thereby increasing the mileage of transport by 113.3 km. The total mileage of transport of aircraft taking off from rescue point 2 is 2,848.7 km. This value is 400.5 km greater than that of the optimal solution of Lingo.
In this study, aircraft scheduling plans with or without influences of random wind were discussed. Through the data analysis based on Table
Transport times with and without random wind.
Transport times without random wind/(h) | Total transport times without random wind/(h) | Transport times with random wind/(h) | Total transport times with random wind/(h) | |
---|---|---|---|---|
Area 1 | 1.528 | 7.488 | 1.558 | 7.733 |
3.03 | 3.126 | |||
2.93 | 3.049 | |||
Area 2 | 0.865 | 12.619 | 1.233 | 14.335 |
3.358 | 3.964 | |||
8.396 | 9.138 | |||
Area 3 | 1.528 | 6.908 | 1.877 | 7.462 |
2.865 | 2.991 | |||
2.515 | 2.594 |
In Table
To ensure the validity of the proposed model, we quantitatively analyzed the model in [
Comparison of performance parameters of two models.
| | |
---|---|---|
Proposed model | 29.530 h | 95.98% |
Model in [ | 27.015 h | 87.40% |
Upgrade rate | | |
Table
Flight route is as important as rescue priority in aircraft-aided rescue operations. Flight route is related to rescue efficiency and can exert a significant influence on rescue safety, especially in regions with complex meteorological conditions and frequent occurrences of natural disasters. Considering the practical scheduling problem of aircraft emergency rescue at present, a multiobjective model is established in this study. The model is calculated using Lingo. Finally, the transport times of aircraft with and without the influence of random wind are analyzed on the basis of the data of an earthquake disaster area. The proposed model is compared with the emergency logistics distribution model in [ Prioritizing the objective function of supply satisfaction while maintaining maximum rescue priority satisfaction during the dispatching of emergency resources can considerably reduce unnecessary economic losses, thus improving the integrated dispatching efficiency. The proposed model reduces economic cost indirectly through the reasonable allocation of relief supplies and planning of the shortest route. Scheduling time is important during emergency rescue. In this study, we focus on the shortest route planning and aircraft scheduling based on rescue priority to shorten the rescue time indirectly. The data involved in the proposed model can be adjusted according to a specific problem. Rescue priority and supply demands can be set according to disaster prediction information on different regions, thus enhancing the rescuing effect.
Nevertheless, there is still a great potential for improving the authenticity and effectiveness of the optimization model. Random wind on flight track is considered in this study, and the influence of multiple complicated weather conditions on aircraft scheduling is ignored. In the next step, the influence of some special weather conditions, such as thunderstorm and dense fog, could be add into the constraints. The course angle of aircraft was equal to track angle in the optimization model, and the flight route planning is simplified. In order to fit the actual flight scene more, flight process can be more refined in future research. We provided initial disaster data for the optimization model in this paper. Real-time and accurate information of survivals and materials in traffic networks is needed to be acquired in the future. In future studies on aircraft scheduling, we can combine flight conflict detect and conflict resolution, as well as a barrier-overcoming flight strategy, to develop highly accurate flight plans on the basis of flight route and to increase the accuracy of rescue dispatching. It will have a high theoretical value and practical significance.
Group set of devastated points
Rescue point
Type of relief supplies,
Total number of rescue points
Total number of aircraft
Total number of devastated points.
Number of devastated points aided by rescue point
Number of random wind test points in the
Maximum payload of the
Maximum fuel load of the
Average fuel consumption rate of the
Devastated point
Rescue priority of devastated point
Time-varying demands for material
Minimum time-varying demands for material
Time-varying supply of material
Weight of material
Number of devastated points served by the
Order of devastated point
Distance between devastated points
Distance between the rescue point and the devastated point
On-off variable, representing whether the
Average flight speed of the
Actual flight speed of
The authors declare that there is no conflict of interests regarding the publication of this paper.
This study was supported by the Fundamental Research Funds for the Central Universities (no. NS2016062).