Introduction

The protection of human life and material assets is the main task of civil aviation [1]. To achieve this task, a set of organizational, technical and regulatory factors has been developed to minimize the risks of aviation accidents associated with the acts of unlawful interference, serviceability and reliability of technical equipment, human factors, and others [2,3].

Today, civil aviation is a system of interconnected systems aimed at ensuring the flight operations of aircraft. It has a hierarchical structure, which includes aircraft, equipment, resources, aviation enterprises, and others.

Modern intelligence technologies play a key role in optimizing processes at aviation enterprises. Due to the rapid development of the aviation industry, increasing efficiency and reducing costs are becoming a priority for aviation enterprises. The use of intelligent control systems allows automating routine processes, which significantly reduces the likelihood of human error and increases the accuracy of operations. These technologies also contribute to improved forecasting and planning, providing more accurate and timely decision-making.

It is worth noting that analytical tools based on artificial intelligence (AI) are capable of processing large arrays of data, identifying hidden patterns and trends, which contributes to the strategic development of enterprises. In addition, intelligent technologies can improve safety by monitoring and analyzing the technical condition of aircraft in real time. This allows for early detection of potential malfunctions and prevention of emergencies. The implementation of such solutions helps to increase the competitiveness of enterprises in the global market. In general, modern intelligent technologies are an integral part of the successful operation and development of aviation enterprises in the modern world.

The use of modern intelligent technologies in the system of maintenance and operation of aviation equipment is a promising area that, unfortunately, has not yet been sufficiently explored.

Despite the obvious benefits, such as improved diagnostic accuracy, fault prediction, and optimized maintenance, the lack of empirical data makes it difficult to implement intelligent systems in practice. This leads to the fact that aviation enterprises are forced to rely on traditional maintenance methods that are less efficient and more resource-intensive. In addition, insufficient attention to the integration of the new technologies can reduce the level of flight safety and reliability of aviation equipment. Further research is needed that would cover various aspects of the use of intelligent technologies, from data collection and analysis to real-life examples of their application in the aviation industry. This would allow for the development of clear recommendations and standards for aviation enterprises, especially in reducing the cost of operating equipment.

Thus, expanding research in this area is critical to improving the efficiency and safety of maintenance and operation of aviation equipment.

State of the art and the statement of the problem

Integration of modern management technologies allows automated monitoring of equipment condition, increasing diagnostic accuracy and timeliness of repairs. The use of analytical tools helps to predict and prevent possible malfunctions, which significantly reduces risks. In addition, optimized business processes contribute to the efficient use of resources and reduce maintenance costs. The implementation of the standards and regulations in maintenance processes ensures compliance with international safety requirements [4,5].

The article [6] determines that intelligent technologies for managing the processes of maintenance and operation of airline equipment, which use artificial intelligence, automation, big data analysis and other advanced technologies for optimization, receive greater financial benefits than those that use traditional methods of equipment operation.

Improving the financial position of the airline company can be achieved through better quality of services, resource-saving methods, material and technical development, and social programs [7].

Paper [8] established that aviation enterprises that enter the market with innovative business processes and an appropriate competitive strategy have significant market advantages and can set their own rules with a strong competitive advantage over competitors.

An analysis of the literature in the field of aviation equipment operation shows that researchers are currently focused on the following problems:

1. Reliability analysis at the stages of operation beyond the determined useful life of the equipment [9,10]. 2. Development of intelligent data processing methods using artificial intelligence tools [11,12]. 3. Minimization of expendable resources [13,14]. 4. Synthesis and analysis of decision-making procedures regarding the condition of equipment and components of the operating enterprise [15,16]. 5. Optimizing the spare parts inventory and the organizational structure of their deployment [17,18]. 6. Optimization of operation processes [19,20].

Civil aviation enterprises usually spend significant financial resources to support the operation of aviation equipment [21]. Most of these costs are related to the remuneration of the personnel of the operating companies, the purchase of auxiliary equipment for the operation processes, storage and transportation of spare parts of equipment. These costs form the tariff rates for maintenance 𝐶 𝑀 and repair 𝐶 𝑅 procedures by the type of used equipment [22,23].

When solving the problem of minimizing operational costs, it is quite logical to choose the total operating costs 𝐶 Σ or average specific operating costs 𝐸(𝐶 Σ 𝑇 Σ ⁄ ) per observation interval 𝑇 Σ as an indicator of efficiency [24,25].

Average specific operational costs can be minimized based on the following considerations. Too frequent maintenance, on the one hand, leads to a high level of reliability, but, on the other hand, is characterized by high operational costs. A small number of maintenance activities reduces the reliability of the equipment and is also characterized by high total costs due to a much higher repair tariff rate. Therefore, the optimal number of maintenance procedures can be determined. This approach fits within the framework of the concept of preventive maintenance [26].

During the preventive maintenance, the decision to perform it is made on the basis of data processing using datasets on diagnostic variables of the equipment. We assume that these parameters are characterized by a stochastic model 𝑀 𝐷𝑉 and the processing algorithms form a vector 𝐴 ⃗ . We assume that the cost of implementing one processing procedure is spent with a tariff rate 𝐶 𝑃 . Equipment failure occurs when the values of the diagnostic variables exceed the operational tolerance 𝑣 𝑂 and the preventive maintenance is implemented when variables exceed the preventive tolerance 𝑣 𝑀 . The process of failure is characterized by a stochastic model 𝑀 𝐹 . In addition, a number of limitations may be imposed on the aviation company-operator, which are characterized by the set 𝐿. Therefore, the efficiency indicator can be represented as the functional dependence of the following form

𝐸(𝐶 Σ 𝑇 Σ ⁄ ) = Ψ(𝑀 𝐷𝑉 , 𝑀 𝐹 , 𝐴 ⃗ , 𝐶 𝑀 , 𝐶 𝑅 , 𝐶 𝑃 , 𝑣 𝑂 , 𝑣 𝑀 |𝐿 ).(1)

The main task is to determine a preventive tolerance that minimizes the average specific operating costs, i.e.

𝐸(𝐶Σ 𝑇 Σ ⁄ ) 𝑜𝑝𝑡𝑖𝑚𝑎𝑙 = min 𝑣 𝑀 Ψ(𝑀 𝐷𝑉 , 𝑀 𝐹 , 𝐴 ⃗ , 𝐶 𝑀 , 𝐶 𝑅 , 𝐶 𝑃 , 𝑣 𝑂 , 𝑣 𝑀 |𝐿 ).(2)

Thus, the purpose of this paper is to optimize the operational costs of the aviation enterprise when monitoring the diagnostic variables of equipment. In this case, the main attention will be paid to the analytical solution of the optimization problem within the framework of the assumptions made about the models of the diagnostic variables, the model of failure occurrence and the adopted data processing algorithms.

Intelligence technologies during equipment operation

The use of intelligent technologies in the management system of maintenance and operation of equipment at aviation enterprises helps to increase productivity, reduce costs, and improve the overall competitiveness of the enterprise in the global market. The key opportunities for their application in the aviation sector are summarized in Table 1. In the context of the research problem, it is possible to identify the key advantages of using modern intelligent technologies in the management system of maintenance and operation of aviation equipment:

1. Because of the use of intelligent technologies (AI and big data analysis), it is possible to accurately predict possible failures and plan their elimination in time, which reduces equipment downtime and increases its availability. 2. Intelligent systems allow for efficient management of spare parts, rational allocation of personnel time, and minimization of maintenance costs. 3. With real-time monitoring and response systems, potential security threats can be quickly identified and timely remedial action can be taken. 4. Automation of routine tasks and the use of intelligent systems help free up time to perform more complex and strategic tasks, which increases their efficiency and job satisfaction. 5. The integration of various data and analytical tools allows to optimize the maintenance and operation schedule, coordinate the work of various departments, and minimize equipment downtime through optimal planning.

6. Failure prediction systems and regular monitoring of equipment conditions allow to timely detect and eliminate problems, which increases equipment availability. 7. The use of intelligent systems allows to efficient collect, process, and analyze operational data, which helps to improve reporting and make informed decisions. 8. Real-time monitoring and analysis of data allows to quickly identify problems and changes in the condition of the equipment, which can help to quickly respond and take the necessary measures to solve them [27 29]. Thus, the introduction of modern intelligent technologies in the aviation equipment maintenance and operation management system is a critical step for airlines to improve the efficiency, safety and reliability of their operations, reduce costs and increase customer satisfaction with flight services.

Method of operational costs optimization

Let us consider the problem of optimizing operational costs for the case of monitoring the diagnostic variables of aviation equipment. To do it, we will accept a number of restrictions on the parameter models and the failure process:

1. One diagnostic variable is subject to monitoring. Let this variable be the voltage at a certain control point of aviation radio equipment. 2. Monitoring is performed discretely with a sampling interval of ∆ and the cost of a single processing procedure 𝐶 𝑃 . 3. The diagnostic variable has two components: deterministic and random. The deterministic component has the form of a steady signal that corresponds to the standard initial value 𝑢 0 . The random component is caused by the influence of thermal noise, instability of power supplies, and the presence of errors in measuring equipment. 4. The random component 𝑛 𝑖 of the diagnostic variable can be characterized by a normal distribution law with zero mathematical expectation and a given standard deviation 𝜎. 5. The pre-failure state is characterized by a violation of the stationarity of the trend of the diagnostic variable change. The transition from the state of normal functioning to this state occurs at a random moment of time 𝑡 𝐵𝐹 . The value of 𝑡 𝐵𝐹 can be described by a uniform distribution law in the range of possible values [𝑡 𝐵𝐹 𝑚𝑖𝑛 ; 𝑡 𝐵𝐹 𝑚𝑎𝑥 ]. 6. The pre-failure state causes a linear change in the diagnostic variable over the time. The slope of the linear trend 𝛾 is random. The value of 𝛾 can be described by a uniform distribution law in the range of possible values [𝛾 𝑚𝑖𝑛 ; 𝛾 𝑚𝑎𝑥 ]. 7. Failures are independent, which does not require additional procedures for processing correlation dependencies [30,31]. 8. The duration of preventive maintenance is a deterministic value and is equal to 𝜏. 9. After maintenance or repair, the value of the diagnostic variable will be equal to the value 𝑢 0 .

Based on these assumptions, a mathematical model of the diagnostic variable can be written in a discrete form

𝑢 𝑖 = 𝑢 0 + 𝑛 𝑖 + tan (𝛾)(𝑖 − 𝑡 𝐵𝐹 )𝜙(𝑖 − 𝑡 𝐵𝐹 ),(3)

where 𝜙(𝑖) is the step function.

To evaluate this model, regression analysis methods can be used, in particular those studied in [ 32 34].

For the cases when 𝑖 < 𝑡 𝐵𝐹 , the diagnostic variable will be described by a normal law with mean 𝑢 0 and standard deviation 𝜎 because of linear functional transformations. In the case of the prefailure condition, taking into account the independence of the set of random variables 𝑛 𝑖 , 𝑡 𝐵𝐹 and 𝛾 and using the methods of functional transformations, the probability density function of the diagnostic variable can be presented as follows

𝑓(𝑢) = ∫ ∫ 𝑓(𝑛) tan (𝛾) 𝑓(𝑡 𝐵𝐹 )| 𝑡 𝐵𝐹 =𝑖− 𝑢−𝑢 0 −𝑛 tan(𝛾) 𝑑𝑛𝑑𝛾.(4)

The efficiency indicator (1) can be written in the following form

𝐸(𝐶 Σ 𝑇 Σ ⁄ ) = 𝑞 𝑀 𝐶 𝑀 + 𝑞 𝑅 𝐶 𝑅 ∑ 𝑡 𝑀 𝑗 𝑞 𝑀 𝑗=1 + 𝑞 𝑀 𝜏 + ∑ 𝑡 𝐹 𝑗 𝑞 𝑀 𝑗=1 + 𝑞 𝑅 𝑡 𝑅 ,(5)

where 𝑞 𝑀 and 𝑞 𝑅 are the average number of maintenance and repair procedures per observation interval, 𝑡 𝑀 𝑗 and 𝑡 𝐹 𝑗 are the moments when the diagnostic variable exceeds the preventive and operational thresholds, 𝑡 𝑅 is the average repair duration.

In this view, it can be assumed that failure will occur when there is insufficient time to perform preventive maintenance in the case if the diagnostic variable changes from the preventive to the operational threshold. To solve the problem (2), we use model (3) for the moments of time 𝑡 𝑀 𝑗 and 𝑡 𝐹 𝑗 , resulting in

𝑡 𝑀 𝑗 = 𝑣 𝑀 − 𝑢 0 tan (𝛾) + 𝑡 𝐵𝐹 − 𝑛 𝑖 tan(𝛾) ,(6)𝑡 𝐹 𝑗 = 𝑣 𝑂 − 𝑢 0 tan (𝛾) + 𝑡 𝐵𝐹 − 𝑛 𝑖 tan(𝛾) ,(7)

where 𝑛 𝑖 ̃ is the error value of the measuring equipment at the moment of exceeding the preventive threshold.

The maximum time resource for failure elimination and preventive maintenance carrying out will be determined as

𝑡 𝑚𝑎𝑥 𝑗 = 𝑡 𝐹 𝑗 − 𝑡 𝑀 𝑗 = 𝑣 𝑂 − 𝑣 𝑀 + 𝑛 𝑖 ̃− 𝑛 𝑖 tan(𝛾) .(8)

Let's assume that the monitoring uses equipment of a high accuracy class, then σ ≪ 1. Then formula (8) will be simplified

𝑡 𝑚𝑎𝑥 𝑗 ≈ 𝑣 𝑂 − 𝑣 𝑀 tan(𝛾) .(9)

To find the estimates 𝑞 𝑀 and 𝑞 𝑅 we first determine the probability density function for 𝑡 𝑚𝑎𝑥 𝑗 . To do this, we write the inverse function to ( 9)

𝛾 = arctan ( 𝑣 𝑂 − 𝑣 𝑀 𝑡 𝑚𝑎𝑥 𝑗 ).(10)

In this case, the Jacobian of the transformation is equal to the modulus of the derivative of function (10) and is equal to

𝐽 = | 𝑑𝛾 𝑑𝑡 𝑚𝑎𝑥 𝑗 | = 𝑣 𝑂 − 𝑣 𝑀 𝑡 𝑚𝑎𝑥 𝑗 2 + (𝑣 𝑂 − 𝑣 𝑀 ) 2 .(11)

Therefore

𝑓(𝑡 𝑚𝑎𝑥 𝑗 ) = 1 𝛾 𝑚𝑎𝑥 − 𝛾 𝑚𝑖𝑛 𝑣 𝑂 − 𝑣 𝑀 𝑡 𝑚𝑎𝑥 𝑗 2 + (𝑣 𝑂 − 𝑣 𝑀 ) 2 .(12)

The average number of maintenance and repair procedures is determined from density (12) by determining the integral from zero to 𝜏 and the integral from 𝜏 to infinity. As a result of solving the equations, we can get the estimates of the form

𝑞 𝑀 = 𝑞 Σ 𝛾 𝑚𝑎𝑥 − 𝛾 𝑚𝑖𝑛 ( 𝜋 2 − 𝛾 𝑚𝑖𝑛 − arctan ( 𝑡 𝑚𝑎𝑥 𝑗 𝑣 𝑂 − 𝑣 𝑀 )),(13)𝑞 𝑅 = 𝑞 Σ 𝛾 𝑚𝑎𝑥 − 𝛾 𝑚𝑖𝑛 (arctan ( 𝑡 𝑚𝑎𝑥 𝑗 𝑣 𝑂 − 𝑣 𝑀 ) − 𝜋 2 + 𝛾 𝑚𝑎𝑥 ),(14)

where 𝑞 Σ is the average total number of maintenance and repair procedures. After using the operations of averaging, finding the statistical characteristics of the tangent of the random slope of the linear trend and using equations ( 13) and ( 14), the observation interval (numerator in equation ( 5)) can be presented as follows

𝑇 Σ = 𝑞 Σ (𝑎 1 + 𝑎 2 𝑣 𝑀 + 𝑎 3 arctan ( 𝑡 𝑚𝑎𝑥 𝑗 𝑣 𝑂 − 𝑣 𝑀 ) + 𝑎 4 𝑣 𝑀 arctan ( 𝑡 𝑚𝑎𝑥 𝑗 𝑣 𝑂 − 𝑣 𝑀 )),(15)

where 𝑎 1 , 𝑎

The last step of the calculation is to analyze function (18) for the presence of a minimum with respect to the preventive threshold 𝑣 𝑀 . The analysis showed that this dependence has one minimum. The complex nature of formula (18) necessitated the use of numerical optimization methods to find the optimal preventive threshold.

The flowchart of proposed method is shown in Figure 1.

Results and discussions

For the practical testing of the proposed method of optimizing the operational costs of the aviation enterprise, statistical modeling was carried out. The primary data for modeling were obtained by analyzing statistical reports and activities of three aviation enterprises:

-ZEFKO UKRAINE LLC.

--PJSC "DHL International Ukraine" [ 35 37].

The central repair center for spare parts and equipment is located at a long distance from the enterprises, which indicates a rather expensive and lengthy delivery of units with operational equipment failures. Maintenance procedures were carried out at the airport, which makes it much less expensive compared to repairs.

At the initial stage of the simulation, realizations of one diagnostic variable in the form of a 220 V supply voltage were obtained for 10000 repetition epochs. An example of changing the diagnostic variable is shown in Figure 2.

The graph in Figure 2 was obtained for the initial data:

- In Figure 1, we have one failure elimination when the voltage value does not exceed the operational threshold in the deterioration state, and two failures when this threshold is reached.

The durations of threshold crossings are also random variables. Figure 3 shows a histogram of frequencies for the moments of crossing the operational threshold. Figure 4 shows that the simulation results coincide with the analytical calculations. The minimum points on both graphs also coincide. The optimal value of the preventive threshold, which corresponds to the minimum operational cost, for the determined initial data is 257.48 V. The results of calculations and statistical simulation demonstrate the feasibility of the proposed approach for optimizing operational costs not only for aviation enterprises, but also in other industries.

Conclusions

Thus, the use of modern intelligent technologies in the management system for the maintenance and operation of aviation equipment is very appropriate and promising in the practice of an aviation enterprise. The introduction of intelligent technologies will allow aviation companies to optimize costs, reduce equipment downtime and increase its availability. In addition, they provide improved data management, which contributes to more efficient decision-making and resource planning. Intelligent technologies help to ensure sustainable improvement and innovation in the management system, which allows airlines to provide high quality service and remain competitive in the modern world of the aviation industry. This paper considers the problem of determining the optimal frequency of preventive maintenance in terms of minimizing operational costs. The problem is solved analytically, taking into account the stochastic model of changes in the diagnostic variable in the period immediately before the equipment failure. The obtained analytical equations are confirmed by statistical simulation. The results of the study can be used during the launching new aviation enterprises specialized on maintenance and operation and improve the management of production processes for existing ones.

Future scientific research will be aimed at developing a maintenance system with an adaptive preventive threshold, the value of which will be adjusted to the current trends in the diagnostic variables of aviation equipment.