The paper concentrates on the problem of design of operation system for modern UAV based on statistical data processing procedures. Modern UAV is a complex system that contains mechanical, electronic and aerodynamic components. Operation system performs the function of equipment efficiency and reliability providing. In general case, operation system consists of equipment, processes, personnel, documentation, control and measuring devices, etc. This system structure is considered according to adaptability, control and data processing principles. Adaptability is considered as the main property of the operation system that allows providing efficient UAV intended use in priori uncertainty conditions. Authors substantiate the efficiency indicator that takes into account effectiveness, time resources and costs. The three strategies of operation system elements inspection are considered. The first strategy (catchall inspection) is associated with simultaneous inspection of all elements of operation system. The second strategy (sliding window inspection) provides some predetermined elements inspection. The third strategy (random inspection) is associated with random selection of elements for inspection. Analytical formulas for the third strategy are obtained based on Markov circuit tool. Analysis of three strategies for UAV inspection proved the advantages of catchall inspections.
Today unmanned aerial vehicles (UAVs) are used in different branches of human
activity [
3. Software for UAV’s operational data monitoring (diagnostic variables monitoring and processing, reliability parameters monitoring and processing, decision making about preventive and corrective actions, etc.).
The third option of software is included in the operation system (OS) [
Modern UAV is complex technical system that controlled by several operators. Therefore, the OS of modern UAV should be considered as object of design and improvement.
Analysis showed that the modern challenge during UAV operation is artificial intelligence principles utilization. These principles allow providing efficient intended use of equipment in conditions that had not been taken into account during design stage. 2
Literature [
The OS can be considered as an object of design and improvement especially in
terms of intellectualization [
The sufficient attention is paid to the first and second option of UAV software [13; 14], but the third software option is not enough considered in scientific literature.
More over, the questions of UAV usage in the airspace are not considered in
Ukrainian domestic regulatory documentations in civil aviation branch. The
standardization issues for maintenance and reliability of UAV and other aviation equipment
are presented in [
Methodology of UAV operation system design is considered in [
The corrective and preventive actions are implemented based on the results of
statistical data processing [
The technical condition of UAV can change during operation. This change causes
to nonstationarity in trends of diagnostic variables or reliability parameters. Analysis
of such processes can allow predicting residual life time of UAV. In literature these
problems are called changepoint analysis [
For comparative analysis of statistical data processing results, it is necessary to
choose the efficiency indicator. Different types of efficiency indicator in OS are
considered in [
The aim of operation system is to provide the required level of efficiency at the observation time. This aim can be achieved through statistical data processing procedures usage and corrective and preventive actions generation and implementation.
The OS efficiency is the following function:
Ef f ( A, , R, D / Tobs ) Ef , where A is a vector of statistical data processing algorithms, is a vector of OS components conditions, R is a vector of requirements for OS components, D is a vector of possible decision making, Tobs is a observation time in sliding window, is a range of possible values of efficiency.
In this paper the dependence of efficiency on vector of statistical data processing algorithms will be researched. From mathematical point of view this problem can be solved through choosing the best algorithm A for maximum efficiency providing: f ( A, , R, D / Tobs ) max . 3
The structure of OS is shown in Fig. 1.
Customers Education institutions
International Civil
Aviation Organization
Design organizations UAV manufacturers
Ministry of infrastructure of
Ukraine
Operation organizations Control system for
OS International civil aviation organization generates standards and recommendations for national aviation administration in the branch of UAV operation. Ministry of infrastructure of Ukraine regulates the question of airspace usage by UAV, inspects aviation organizations from the safety point of view, etc.
Customers form requirements for types and characteristics of UAVs. These requirements are taken into account by design and operation organizations. The UAV specialists are trained in education institutions.
Operation organization is the main component of OS structure. Control system for OS inspects UAV components, processes the statistical data, generates and implements corrective and preventive actions.
The control system interacts with all elements in Fig. 1 in case of intelligence principles based mode usage.
The generalized diagram of processing procedure is shown in Fig. 2.
Requirements
UAV OS components
Efficiency estimation for control actions The choice of additional data processing procedures
Conformity assessment Is efficiency
enough? No
Is problem solved?
Yes
Yes No
Formation and implementation of control actions
Operation continuation
Usage of adaptability principles – A3 is an algorithm of parameters stability assessment in case of changepoint; – A4 is an algorithm of preventive and corrective actions formation; – A5 is an algorithm of preventive and corrective actions implementation; – A6 is an algorithm of decision making about efficiency providing after control actions implementation;
– A7 is an algorithm of decision making about additional data processing procedures;
– A8 is an algorithm of decision making about usage of intelligence based procedures; – A9 is an algorithm of statistical processing for diagnostic variables; – A10 is an algorithm of statistical processing for reliability parameters.
Algorithms A7 , A8 , A9 , A10 have complex structure and contain the set of procedures.
All algorithms are generalized. For detailed description of algorithms, it is necessary to solve synthesis and analysis problems, to choice best option for criterion of maximum efficiency, etc. Initial information for synthesis and analysis problems is measured data trends model.
Considered algorithms contain detection, estimation, filtration, extrapolation,
interpolation, and other procedures. There are algorithms with known sample size, and
sequential algorithms. The sequential procedures have advantages in duration of
decision making [
Usage of adaptability principles is based on the following approaches: – logic based solution finding; – fuzzy logic; – Bayesian network; – adaptable learning after observation; – semantic network; – neural network, etc [24; 25].
More over, during diagnostic variables measuring, expert evaluation and subjective
probability based estimates can be used [
There are different types of adaptation: 1) adaptation to the models and models parameters; 2) adaptation to the external conditions; 3) adaptation to internal changes in OS; 4) adaptation to the new requirements of regulatory and normative documents; 5) adaptation to OS aims, etc. 4
Let’s consider the problem of efficiency indicator substantiation based on the analysis of different strategies of UAV OS components inspection. The efficiency indicator takes into account the probability of correct detection of unconformities in the OS and operational costs. In the general case, the numerical values of the efficiency indicator are random variables, so we can use its statistical characteristics, e.g. mean value.
Let the operation system of UAV contains N components. Each component can be in one of two conditions: serviceable and failure.
Serviceable condition corresponds to the case of component compliance with established requirements. Failure condition corresponds to the case without compliance with established requirements. Let the quantity of components with failure is n .
The value n is a discrete random variable in the range [0; N] . The failure can occur with failure rate (t) . Assume that during the inspection, new failures can’t occur. The operational cost of one inspection is C .
The mathematical expectation of the probability of correct detection is defined as: where m1(n) is a mathematical expectation of detected unconformities number, Тobs is an observation interval (the sum of OS functioning time TOS and inspection procedure time t ).
The mathematical expectation of the efficiency indicator can be represented as: m1(D) (t)Тobs m1(n) m1(n) ,
n m1(Ef)
m1(D) Cmax /(Cmax C ) , (1) (2) where C is a total cost for OS components inspections, Cmax is a maximum allowable costs for operation.
Variables m1(D) and m1(Ef) are in the range [0;1] .
Let consider three strategies: 1) catchall inspection (all N elements of operation system are simultaneously inspected during time t ) – CI strategy;
2) sliding window inspection (all N elements of operation system are inspected during m inspection procedure each of which is characterized by time t ) – SWI strategy;
3) random inspection (at each of m inspections, M components are verified randomly so that the total number of verified components is a random variable in the interval [M ; N ] ) – RI strategy.
In the case of CI strategy mathematical expectation of the probability of correct detection and the mathematical expectation of the efficiency indicator can be calculated according to the following equations:
m1(D / CI) m1(Ef / CI)
n (t)TOS t
,
In the case of SWI strategy according to equation (1) and (2) the probability of correct detection and the efficiency can be presented as follows: m1(D / SWI)
, m1(Ef / SWI)
, n (Cmax NC) jp j(m)
j0 m(t)TOS t Cmax .
In this equation p j(m) is a final probability that characterize the random selection of M elements from N among which n elements don’t conform the requirements during m inspections procedures.
The system condition for the random inspection can be described using the graph (see Fig. 3), and the definition of the calculation formulas is carried out using the Markov model, for which the final probabilities are determined on the basis of the transition matrix of conditional probabilities.
The final probability depends on m and can be written as: N where m 1, 1 , Pi j is a conditional probability of j i unconformities detec M tion in the next stage of inspection if i unconformities are detected during previous stages. In this case:
Pi j
(n i)!(N n i)!M!(N M )! ( j i)!(n j)!(M j i)!N!(N n M j)!
Comparing obtained equations for different inspection strategies, it can be concluded that UAV OS efficiency in case of the first strategy of catchall inspection more than efficiency for both considered the second (SWI) and third (RI) strategies, i.e. m1(Ef / CI)) (t)TOS t Cmax m, m1(Ef / SWI) n(Cmax NC)
(t)mTOS t Cmax m1(Ef / CI)) m1(Ef / RI)
n(Cmax NC ) (t)TOS t Cmax
n (Cmax NC ) jp j(m)
j0 m(t)TOS t Cmax
nm n jp j(m) j0 .
So the first strategy of UAV OS components inspection has efficiency exactly in m
times higher compared with the second strategy and at least in m times compared
n
with the third strategy (as jp j(m) n ) [
j0
Let’s consider the numerical example of different strategies efficiency calculation. Let UAV OS contains N 50 components with n 10 unconformities among them. The quantity of inspections m 5 , the time of OS functioning TOS 1000 hours, inspection duration t 4 hours, total costs Cmax 5000 usd, operational cost C 10 usd, failure rate (t) 0.01 unconformity per hour.
So mathematical expectation of detected unconformities number m1(n) 7.051. According to obtained formulas can be get m1(D / CI) 0.996 , m1(Ef / CI) 0.9 ,
So in this case the best option is the strategy of catchall inspection. 5
Analysis showed that not enough attention is paid to systematic review of UAV OS. Therefore, the OS structure is proposed based on system approach and control theory. Authors concentrated on consideration of control system for UAV OS. Control system collects and processes statistical operational data from all OS components; such approach allows making decision about corrective and preventive actions.
The generalized diagram of processing procedure is considered in the paper. This diagram suggests two modes of OS: regular mode and adaptable mode. The adaptability principles utilization expands the possibilities of flexible control of UAV operation. Three strategies of OS components inspection were analyzed. The numerical example showed advantages of catchall inspection.