Keywords

1 Introduction

The utility tunnel is a widely used technology in urban construction, which has the advantages of intensive land use and avoiding repeated excavation of road surfaces. In the construction of new large airports such as Qingdao Jiaodong International Airport and Beijing Daxing International Airport, the construction of utility tunnel is also being considered. However, in the process of apron ground service support, the location and quantity of the apron in-ground pits have a significant impact on the safety and efficiency of apron operations. Currently, research on apron utility tunnel mainly focuses on alignment planning [1, 2], cross-sectional design [35], fueling spigot well optional domains [6], and drainage design [7]. There is relatively little research on the selection of apron in-ground pits locations based on utility tunnel technology from multiple perspectives. Therefore, this paper focuses on the selection of apron in-ground pits locations. Unlike traditional shaft selection, the selection of apron in-ground pits locations needs to consider factors such as the diameter and quantity of pipelines, as well as the service range after extraction. Based on the determination of the target area, cost function, and constraints, the design principles of in-ground pit selection are used to minimize total cost, optimize overall service level, or maximize social benefits, thus determining a rational and efficient in-ground pit network structure. Based on the demand for service support interfaces from aircraft, the paper discusses the establishment of a multi-objective optimization model from the perspectives of economic affordability, operational efficiency, and labor costs. The goal is to obtain the optimal aggregation, location, and quantity of apron in-ground pits, in order to reduce the use of ground support vehicles and improve apron operational efficiency.

2 Multi-objective Optimal Site Selection Model for Apron In-Ground Pits

2.1 Analysis of Factors Affecting the Selection of Apron In-Ground Pits Locations

This paper analyzes the influencing factors of in-ground pits site selection and establishes the cost index system of in-ground pits site selection model consisting of 3 first-level evaluation indexes, including the safety maintenance cost B1, the labor cost B2, and the facility construction cost B3, and 9 s-level indexes, as shown in Fig. 1.

Aircraft in the process of sliding into, launching and safeguarding operations will produce a variety of unsafe factors, the need to optimize the traffic flow of the apron support area, reduce the use of special support vehicles and provide sufficient parking space for other vehicles, effectively reduce environmental pollution at the same time to optimize the allocation of ground resources, therefore the introduction of the safety operation cost C1, the environmental protection cost C2, and the construction distance cost C3 as an evaluation index; The consideration of labor cost mainly focuses on reducing the labor intensity of ground staff and simplifying the service guarantee process, so as to improve the work efficiency. Especially for airports with high labor cost, reducing the number of ground staff will effectively save human resource cost, so the human resource cost C4, the service time cost C5, and the service complexity cost C6 are selected as evaluation indicators. The cost of facility construction takes into account the economic cost in the whole cycle of in-ground pits construction, such as the development of infrastructure, equipment configuration, and maintenance of in-ground pits, can effectively reduce energy demand and operating costs in the long run. This helps in saving airport operational expenses and material consumption. Therefore, the evaluation criteria include the land development cost C7, the pipeline laying cost C8, and the in-ground pits installation cost C9.

The weights and rankings of the first-level and second-level indicators are obtained through expert scoring and consistency tests, as shown in Table 1.

From the Table 1, it can be seen that the in-ground pits device cost C9, the human resource cost C4 and the construction distance cost C3 have the greatest influence on the in-ground pits site selection, and the optimization calculation of these three objectives can get the better result of the site selection of in-ground pits.

Fig. 1.
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Site Selection Model Cost Indicator System

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Table 1. Ranking of Criteria Weights
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2.2 Model Building

Most of the siting problems through the alternative set of points for discrete siting, but in practice the siting problem is often carried out in continuous space, that is, the demand point is in continuous space and the facility can be located anywhere in the space. Continuous siting problem is usually difficult to calculate and model. Some scholars have proposed methods to solve the siting problem, which can be summarized as follows: 1) Abstract the continuous space demand object into points, lines or polygons; 2) Adopt some rules to transform the infinite facility candidate points into a finite set of points; 3) Adopt a discrete siting model for siting [8]; This paper adopts a method of transforming a continuous plane into a finite set of points, discretizing the continuous plane of the machine position to obtain a finite set of candidate facility points. Based on this, the article combines the maximum set cover model and the P-median model to establish a multi-objective site selection model for apron well. The decision variables are as follows:

$${\text{X}}_{\text{j}}\text{=}\left\{\begin{array}{c}{1}\text{,} \, \, {\text{s}}{\text{e}}{\text{t}} \, {\text{i}}{\text{n}}-{\text{ground}} \, {\text{pits}} \, {\text{head}} \, {\text{at}} \, {\text{j}}\\ {0}\text{,} \, \, {\text{else}}\end{array}\right.$$
(1)
$${\text{Y}}_{\text{ij}}\text{=}\left\{\begin{array}{c}{1}\text{,} \, \, {\text{j}} \, {\text{serves}} \, {\text{docking}} \, {\text{port}} \, {\text{i}}\\ {0}\text{,} \, \, {\text{else}}\end{array}\right.$$
(2)

The site selection of the apron in-ground pits has special characteristics. It needs to achieve full coverage of aircraft service interfaces with the minimum number of in-ground pits, while also considering optimization issues in practical application scenarios. In multi-objective optimization, it is necessary to consider the trade-off relationship between multiple objectives. This relationship is usually controlled using weights (λ) to transform the multi-objective problem into a single-objective optimization problem. However, this problem has a characteristic that differs from traditional optimization methods, that is, once the location of the in-ground pits is determined, it is difficult to change. Therefore, in the selection process, it is necessary to determine the weight relationship between several objectives, meaning that for a specific implementation plan, the weights between several objectives are always static. This problem focuses on three types of cost: the construction distance cost, the human resource cost and the in-ground pits installation cost.

The In-Ground Pits Installation Cost

In-ground pits device is the integration of various types of pipeline equipment, which can be equipped with a single pipeline or multiple pipelines in one in-ground pit, the higher the integration, the fewer the construction quantity and the lower the cost. But the work site is more complex, the integration and construction quantity of the in-ground pits need to be considered comprehensively. According to the different integration levels of the pipelines, the construction cost of the in-ground pits varies as shown in (3).

$${\text{M}}_{\text{j}}{=2.5*}\sum_{{\text{i}}\in{\text{I}}}{\text{Y}}_{\text{ij}}{+2.5}$$
(3)

The Construction Distance Cost

The construction distance is the distance from in-ground pits to the aircraft service interface. Due to the different pipe diameters, the service distance for larger diameter pipelines should be shorter during construction, while the service distance for smaller diameter pipelines can be appropriately extended. The combination of pipelines with different diameters has a significant impact on the construction distance of in-ground pits facilities. In summary, the larger the service distance, the lower the work efficiency. The Euclidean distance is used in the model.

$${\text{d}}_{\text{ij}}{=}\sqrt{{{\text{(x}}_{\text{i}}-{\text{x}}_{\text{j}}{)}}^{2}{+}{{\text{(y}}_{\text{i}}-{\text{y}}_{\text{j}}{)}}^{2}}$$
(4)

The Human Resource Cost

In practical operations, a certain number of staff members are needed to handle the connection and conveyance of various interfaces. The specific cost of human labor services is difficult to calculate accurately. This paper uses the number of staff as a measure, with one worker assigned to each apron in-ground pit. As the number of staff members increases, so does the associated cost.

Combining the above 3 costs yields the model as follows:

$$ {\text{MinZ = }}\alpha {{*}}\mathop \sum \limits_{{\text{j}} \in {\text{J}}} {{\text{M}}_{\text{j}}}{{*}}{{\text{X}}_{\text{j}}}{{ + }}\beta {{*f*}}\mathop \sum \limits_{{\text{i}}\varepsilon {\text{I}}} \mathop \sum \limits_{{\text{j}}\varepsilon {\text{J}}} {{\text{d}}_{{\text{ij}}}}{{*}}{{\text{Y}}_{{\text{ij}}}}{{ + }}\gamma {{*k*}}{{\text{X}}_{\text{j}}}$$
(5)
$${\text{N}}\left({\text{i}}\right){=}\left\{{\text{j}}\in\text{J|}{\text{d}}_{\text{ij}}\leq{\text{D}}_{\text{i}}\right\}$$
(6)
$${\text{Y}}_{\text{ij}}{\leq}{\text{X}}_{\text{j}}{,}{\forall}{\text{i}}{\in}\text{I},{\forall}{\text{j}}{\in}{\text{J}}$$
(7)
$$\sum\nolimits_{{\text{i}}{\in}{\text{I}}}{\text{Y}}_{\text{ij}}{\leq}{\text{X}}_{\text{j}}{,}{\forall}{\text{j}}{\in}{\text{J}}$$
(8)
$$\sum\nolimits_{{\text{j}}{\in}{\text{N}}\left({\text{i}}\right)}{\text{Y}}_{\text{ij}}={1},{\forall}{\text{i}}{\in}{\text{I}}$$
(9)

In (5): I is the set of aircraft service interfaces, that is, demand points \({\text{i}}\), and J is the set of in-ground pits facility candidate points j; dij is the distance from in-ground pit j to aircraft service interface i; Di denotes the acceptable service radius of interface i; and α, β, and γ are the weights of each cost, the values of the three are determined by the weights of the corresponding indicators calculated in Table 1, and α + β + γ = 1. k stands for manual salary, the specific value of which is determined on a case-by-case basis.

In this model, if an aircraft service interface is located within the service range of one or more in-ground pits facilities, it is considered to be covered. (7) indicates that interface can be provided only when in-ground pit is established, and (8) indicates that at least one aircraft interface is serviced by any in-ground pits. In a single aircraft position, only one in-ground pit with the same function needs to be established for simplification. (9) ensures that aircraft service interface is serviced by only one in-ground pit. Due to the different magnitudes of construction cost and distance cost in the model, a cost coefficient f is introduced for normalization: f = 1.

2.3 Algorithmic Solution

In order to solve the above modeling problem, this paper uses the particle swarm algorithm, which is designed by simulating the feeding behavior of bird flocks, starting from a set of random particle positions, and seeking the optimal position of particles through continuous iteration [9]. In the site selection problem, the position of each particle is regarded as the position of the candidate point, and the advantages and disadvantages of the point can be evaluated by calculating the fitness function value of each particle, and the point with the highest fitness can be obtained as the final site selection point after continuous iteration, particle swarm algorithm flow as Fig. 2.

Fig. 2.
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Particle Swarm Algorithm Solution Process for In-ground Pits Siting Models

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3 Example Analysis

3.1 Data Processing

In this paper, the selection of class C aircraft as the design aircraft, according to the Civil Airport Flight Area Technical Standards [10] provisions, class C aircraft on the apron net distance should not be less than 4.5 m, the in-ground pits in the service need to be raised, so the distance from the aircraft should not be less than the maximum value specified, the in-ground pits of the feasible domain should be outside the airfield security line.

The service radius of the pipelines in the in-ground pits is also specified. The diameter and service radius of the pipelines may vary according to different aircraft types, system designs and operational requirements, and may be adjusted as needed during actual work. This paper uses empirical data as a reference.

Referring to the provisions in MHT6031–2018 [11] and Civil Aircraft Oxygenation [12]: the length of the oxygenation hose should be not less than 10 m, and the distance of the oxygenation equipment from the aircraft should not be less than 2 m; MHT6014–2018 [13] stipulates that the inner diameter of the potable water hose should be 25 mm, and the length should be not less than 5 m; MHT6015–2014 [14] stipulates that the inner diameter of the sewage truck receiving hose should be 100 mm and the length should be not less than 5 m; according to Aircraft Ground Equipment Operator, the cable length of the power supply unit to the external power connector of the aircraft should be not less than 10 m. The diameter of air conditioning ducts ranges from 100 to 914 mm, and the effective working distance is 15 m [15]; the diameter of the hoses for compressed air sources ranges from 26 to 76 mm, and their extraction length is about 40 m. Taking the B737-NG as an example and referring to the aircraft type manual, the interfaces required by the aircraft are shown in Fig. 3, and specific data are located in Table 2.

Fig. 3.
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Particle Swarm Algorithm Solution Process for In-ground Pits Siting Models

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Table 2. Service Radius of Each Pipeline
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3.2 Aircraft Parking Stand Layout Mode

The aircraft positions are arranged continuously along the terminal shoreline, and the following situations often occur:

  • For the distal end of the finger corridor terminal building may appear to arrange only a single-airplane position.

  • For the forefront-type terminal building, the aircraft parallel to each other.

  • For the finger corridor terminal building, the bottom of the finger often forms a harbor area, and the head of the aircraft points to the two finger corridors respectively to form a tail concentration.

The three aircraft layout patterns are shown in Fig. 4, and the above three types of aircraft combinations are modeled and solved.

Fig. 4.
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Coordinate System and Corresponding Service Interface Position of Class C aircraft

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3.3 Calculation Result

The results of the calculations for three different aircraft parking stand layout modes are as follows: As Fig. 5(b), the fitness evolution curve reaches the optimal solution within 20 iterations, and as Fig. 5(a), for a single aircraft parking position, the integrated in-ground pit No.1 is located on the right side of the aircraft, providing services to aircraft service interfaces A and B. Integrated in-ground pit No.2 integrates the air conditioning and compressed air pipelines, providing services to aircraft service interfaces C and D. Similarly, integrated in-ground pit No.3 provides services to aircraft service interfaces E and F, achieving the integration of the single aircraft parking position in-ground pit.

When the model converges, the number of iterations is less than 40, which proves that the algorithm is very efficient, as Fig. 6(b). In the case of parallel aircraft parking positions, as Fig. 6(a), the service interfaces A and B of the aircraft on both sides share integrated in-ground pit No.1. The service interfaces C and D of the aircraft are limited by the service radius and cannot be shared between the two sides, therefore, they are provided by integrated in-ground pits No.2 and No.3 located on both sides. Integrated in-ground pit No.4 integrates sewage and clean water services, supplying the left side service interfaces E and F, while integrated in-ground pit No.5 serves the right aircraft service interfaces E* and F*.

In the case of harbor aircraft parking positions, the model iterates less than 20 times to reach the optimal solution. As Fig. 7(a), the service interfaces A and B of the aircraft on both sides share integrated in-ground pit No.1. The service interfaces C and D are similar to the parallel aircraft parking position, provided by integrated in-ground pits No.2 and No.3 located on both sides. Integrated in-ground pit No.4 simultaneously supplies the service interfaces E and F for aircraft on both sides.

From the Fig. 8, it can be seen that regardless of the layout mode, the total cost of the site selection model is always less than the total cost of the traditional site selection for Zhuhai Airport. After calculation, it is found that compared to the traditional site selection for Zhuhai Airport, the site selection model has reduced costs by approximately 50.47%, 52.97%, and 34.01% in different layout modes, effectively achieving the cost-saving goal. At the same time, the comparison of costs among the three groups of the same layout mode shows that in the total cost composition, this study pays more attention to the proportion of the in-ground pits installation cost and the human resource cost, and the final result also proves that the site selection model effectively reduces these costs.

Fig. 5.
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Calculation Results for Single-Airport Integrated In-ground Pits

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Fig. 6.
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Calculation Results for Parallel-Airports Position Integrated In-ground Pits

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Fig. 7.
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Calculation Results for Habor-Airports Position Integrated In-ground Pits

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Fig. 8.
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Comparison of Site Selection Model and In-Ground Pits Costs at Zhuhai Airport under Three Aircraft Layout Models

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4 Conclusions

This paper uses the Analytic Hierarchy Process to identify the key factors that have the greatest impact on the selection of apron in-ground pit location. These factors include construction distance cost, human resource cost, and in-ground pits installation cost. By combining the Maximum Coverage Set model and the P-median model, a multi-objective optimization site selection model is established. The model is then computed using the Particle Swarm Optimization algorithm. The results indicate that in the three layout modes of single aircraft position, parallel aircrafts position, and harbor aircrafts position, the total cost of apron in-ground pits can be effectively reduced. This allows for the consolidation of various service pipelines and the innovative sharing of apron in-ground pits between adjacent stand, further reducing the use of ground support vehicles and personnel. This has practical significance for unmanned apron construction and low-carbon airport development.

There are still some shortcomings in this study: Firstly, AHP is subjective and its consideration of index judgment matrix is limited. Secondly, this paper uses Euclidean linear distance to indicate the path of service pipeline, but there may be some deviation in the actual situation. Therefore, in the future research, we can further explore the problem of in-ground pits based on utility tunnel technology.