Keywords

1 Introduction

Every year, the construction industry is increasingly using new tools and technologies, and unmanned aerial vehicles (UAV) are proof of this. Quadcopters in construction make it possible not to disrupt the technological processes on the construction site during monitoring, they are controlled remotely and change the viewing points, allowing getting objective evidence in real time without interrupting the progress of work. Monitoring large-scale objects such as gas pipelines, bridges, and unique buildings with complex geometries in traditional form from the ground is time-consuming and endangers human life and health. The use of UAV in such cases is more justified. Detection of possible violations during construction, control of the accuracy of installation of structures, compliance with project documentation, detection of defects – all this can be done remotely using quadcopters, really saving time and financial costs. Thus, today there are many options for using UAV in construction and every year the scope of their activities is expanding [1, 2].

In the construction industry, there is a very high probability of all sorts of risks that lead to contradictions between contractors. The most common cases are the resolution of disputes in the performance of contractual obligations. Parties who are involved in conflicting relationships rarely come to a solution on their own [3].

In such cases, control checks are one of the main ways to detect violations in the system of execution of contracts for construction and reconstruction, current and heavy repairs of capital construction objects and to ensure the principle of efficient use of the customer’s funds [4]. The purpose of such a control check is to assess and establish the reliability of the volume and cost of work performed on capital construction projects, as well as to identify the compliance of the quantity and parameters of materials actually used and installed equipment.

The paper provides recommendations on the use of UAV and provides the results of measuring the work performed on an object that has a non-standard complex geometric shape. The need for such an assessment arose during a dispute between the customer and the contractor about the volume of construction and installation works performed and the amount of their payment [6].

2 Methods and Materials

Examination of large or hard-to-reach buildings and structures, which include the object under investigation – the roof of an indoor water park – requires specialized equipment and highly qualified personnel. Specially trained personnel, such as mountain climbers, can access hard-to-reach structures, but they cannot evaluate the site based on the nature and scope of the work performed.

Theoretically, this problem can be solved using specialized equipment, machines (scaffolding, tower vehicle, mountaineering), but this will lead to high material costs. At the same time, there are risks associated with ensuring safety when conducting a survey using such equipment.

The paper proposes to solve this problem by using an unmanned aerial vehicle, which will improve the quality of visual inspection and reduce the cost of its implementation.

An indoor water park was presented as an object. The dispute was that the amount of work performed to install the roof of the object under construction did not match the data of the customer and the contractor. To resolve this conflict, it was necessary to measure the finished product. As the object has a complex geometric shape, it is quite labor-intensive to measure it in the usual way, and a number of additional permissions are required. We proposed a method that helped reduce the cost of work, as well as reduce time and labor costs, but it was not inferior in accuracy.

To solve this problem, the method of aerial photography using an unmanned aerial vehicle (UAV) was applied. At the first stage, it was necessary to determine the design characteristics that are necessary for accurate and reliable processing of the photos obtained in the future [5, 7].

As the object is complex in shape and height from 20 to 25 m, and has the shape of a half-moon, it was necessary to calculate the characteristics of the flight task, namely, to calculate the overlap of photos. To create a 3D model of the object, the flyby was performed in orbits, i.e. around the object (Fig. 1).

Fig. 1.
figure 1

Map of the photographing route.

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To overlap photos, they had to switch from a linear intersection to a corner intersection. Source data: R is the radius of the orbit (depends on the size of the object), N is the number of orbits (depends on the height of the object).

The radius of the orbit, based on the size of the object, is chosen so that the distance from the UAV camera to the object is sufficient. In our case, the size of the object in the plan is 150 × 70 m, we take the maximum length and divide it in half, then we increase the obtained value by 1.5 times and get the radius of the orbit. Knowing the radius of the orbit, we calculate the remaining characteristics.

As the object has a complex shape, the distance to the object from the UAV camera will be different. We take the smallest distance, because if the condition for overlapping images is met at the smallest distance, then the greater the distance, the greater the overlap of images (Fig. 2).

Fig. 2.
figure 2

Positions of the cameras and the images overlap.

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3 Results and Discussion

Knowing the characteristics of the UAV, which can be found in the technical data sheet of the product, we calculate the scale of photographing using the formula (1):

$$ {1 \mathord{\left/ {\vphantom {1 {{\text{M}}_{\upphi} }}} \right. \kern-0pt} {{\text{M}}_{\upphi} }} = {{{\text{H}}_{\upphi} } \mathord{\left/ {\vphantom {{{\text{H}}_{\upphi} } f}} \right. \kern-0pt} f}, $$
(1)

where \( {\text{M}}_{\upphi} \) - scale, \( {\text{H}}_{\upphi} \) – the height of the photographing, \( f \) – focal length.

Based on the scale of photographing, we calculate the scale of the image (formula 2), that is, how much of the real size of the object falls on the image:

$$ \begin{aligned} L_{x} = l_{x} \times m, \hfill \\ L_{y} = l_{y} \times m, \hfill \\ \end{aligned} $$
(2)

where \( L_{x} \), \( L_{y} \) – dimensions of the square of the area captured by a single image, \( l_{x} \), \( l_{y} \) – camera matrix size of the camera, \( m \) – the scale of the photograph.

Then, using the required value of the longitudinal and transverse overlap, the longitudinal and transverse bases of photographing are found. Converting from percentages of the image to actual distances on the ground (formula 3):

$$ \begin{aligned} {\text{P}}_{\text{X}} = L_{\text{X}} \times {\text{P}}(\% ) \hfill \\ {\text{P}}_{y} = L_{y} \times {\text{P}}(\% ), \hfill \\ \end{aligned} $$
(3)

where \( {\text{P}}_{x} \), \( {\text{P}}_{\text{y}} \) – longitudinal and transverse overlap of images, \( {\text{P}} \) – required longitudinal overlap of images.

After determining the overlap, we calculate the angle between the centers of the images. The calculation is based on the overlap of images. We find the linear distance between the centers of images using the formula (4):

$$ \alpha = arctg\left( {\frac{0.5 \times l}{r}} \right) \times 2 , $$
(4)

where r – the radius of the object, l – distance between image centers [8].

We set the angular velocity and calculate the required interval for photographing. Next, the received photos were processed in the Agisoft Metashape software product.

Based on the results of photo processing in the software product, an orthophotomap and a 3D model of the object were obtained (Fig. 3).

Fig. 3.
figure 3

3D model of the object.

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The resulting model was used to calculate the roof area of the object (Fig. 4).

Fig. 4.
figure 4

Calculating the area and volume of the model.

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4 Conclusion

Thus, this method made it possible to carry out the necessary measurements without additional costs, significantly reducing the time of work, as well as the cost of these works [9].

The quality of inspection of buildings (structures) of high storeys, complex configuration, difficult to access cannot be ensured without the use of aircraft, and, therefore, the considered option is a promising technology for inspection and monitoring, including the resolution of disputes in the construction industry [10].