This paper presents a reliability-oriented approach for solving structural optimization problem for UAV flight control system. The system and its components reliability is used as the basis for taking optimum design decisions. The proposed optimization technique is based on improved reliability models for the system components and their fault-tolerant configurations. It enables increasing results certainty to find an optimum variant of flight control system structure with minimum expenditure of technical resources, meeting required reliability level, flight duration and regularity of operations, observing principal constraints (weight, power consumption and overall cost), taking different maintenance and repair modes into consideration.
UAVs’ reliability is one of the key factors that impacts on their effectiveness, which
is characterized by their flight duration and regularity of operations. More than a
quarter of all UAV failures are caused by flight control system (FCS) failures [
fault tolerance based on redundancy with use of effective detection and switching devices (DSD); fault avoidance with improvement of failure-critical subcomponents reliability; and forming expedient strategies and modes of maintenance and repair.
All these methods have own advantages and disadvantages, and their application
should be validated in terms of all phases of the FCS life cycle. Above all, reliability
improvement through fault-tolerant FCS configurations is limited to save resources
and meet requirements concerning acceptable weight, size, power consumption,
overall cost and other important UAV characteristics [
Using flight control system with low reliability and without redundancy precipitates completing both operative and line maintenance. In turn, it causes extra staffing of unmanned aircraft system sections with highly skilled maintenance specialists. As result, this approach provides minimum time for UAV withdrawal from operation, and on the other hand, makes increasing in operating and support costs, and lowering mobility of unmanned aircraft system sections. Creation of centralized workshops in unmanned aircraft system units extends the time of UAVs withdrawal from operation that results in decreasing of UAV availability.
Using addition of redundancy can improve reliability as well as increase
maintenance rate (interval between maintenance (operation restoring) works) to the
needed value, for example, mean time of UAV’s overhaul life. In this case, operation
for flight control system can be reduced to the operative forms and its operating and
support costs will diminish. Although, this advantage is accompanied by increasing of
technical resources (weight, size and power consumption), as well as redundancy may
not improve the system reliability if, for instance, DSD have a failure rate below the
acceptable mimimum level [
If simplified reliability models are used for redundancy amount calculation, then in practice the field FCS reliability will be often below expected level, which was determined during design. Moreover, if for FCS reliability estimation the conservative (for example, overestimated on 5-10%) values of reliability parameters are used, then amount of redundancy, and consequently system complexity, expenditure of technical resources, and cost of design, engineering and procurement will unreasonably increase.
Hence, the predicted FCS reliability must corresponds to required level with consideration for specified resource constraints and rationale for appropriate redundancy approach and redundancy amount. Accordingly, in order to make optimum decisions for FCS structure design within a limited time there is necessity to: 1) give grounds for expedient fault-tolerant configurations of FCS components; 2) develop reliability models for FCS fault-tolerant units with a high level of adequacy, in which besides reliability parameters of main and standby parts taken into account:
effectiveness parameters for detection equipment (probability of successful failure detection, rate of false alarm), and diagnostics and switching devices; prediction on the amount of undetected software failures for computer-based modules, and variants of troubleshooting technics;
parameters for maintenance and repair strategies (repair duration and repairs amount); maintenance organization effectiveness parameters; 3) have a structure optimization technique, which includes optimization methods, criteria and constraints. In essence, it is one of the desigh instruments that supports ensuring required reliability level and mission requirements package implementation, including expected UAV's flight duration and operations regularity, with a minimum expenditure of technical-economic resources, as well as observing accepted resources constraints. Moreover, the technique should be based on increasing automation in design decision-making procedures, since the permanent rapid updating of UAV avionics causes the time reduction on its development.
The conducted analysis has shown an absence of above-mentioned models as well as valuable optimization technique that defined actuality of this research. 2
This system contains three main components (Fig. 1) [
Based on structure analysis for UAVs’ flight control systems with variety redundancy techniques, next variants of FCS components design were chosen for research: 1) three design variants for navigation subsystem: the 1st – without redundancy; the 2nd – with bimodal parallel/series redundancy for gyroscopes and accelerometers;
the 3rd – with bimodal series/parallel redundancy for gyroscopes and accelerometers;
2) two design variants for flight computer with majority voting redundancy 2-outof-3 microprocessors (MPs): the 1st – without additional standby MP; the 2nd – with inherent standby MP; 3) three design variants for autopilot: the 1st – without redundancy; the 2nd – with simple parallel redundancy for main elements of control unit, three servo units and power controller, with use majority voting structure (MVS) 2-out-of-3 for each flight surfaces position sensors;
the 3rd – three parallel control units are used instead of two parallel control units additionally to the 2nd variant.
The well-known reliability models for systems with voting logic 2-out-of-3 without
additional standby parts have a sufficient adequacy level [
Pitot tube Pressure and temperature transdusers Air data subsystem (ADS)(ADS) Magnetometer
(MM) GyГroірsоcсoкpоeпG1X
Г іроскоп 2 Gyroscope GY
Гіроскоп GyroПsоcоoсpіeZGZ
Inertial measurement unit (IMU) Ground control station(GСS) Onboard
GPS
filter (KF-1) Microprocessor
MP1 Microprocessor
MP2 Microprocessor
MP3 Microprocessor
MP R Voting unit Fault detector Kalman filter
(KF-2) Flight computer Control Unit
propulsion controller
Servo units
Flight control
surfaces
GСS
Reliability of fault-tolerant units depends not only on reliability of their main and
stanby elements, redundancy technique and amount of redundancy. It also is affected
by effectiveness of equipment, which detects faults, diagnoses and isolates them,
reconfigures such units [
Most of known reliability models for various types of hardware redundancy are
obtained with assumption, that perfect DSD are used to support fault tolerance [
In other models, only effectiveness of imperfect detection or switching devices is
taken into account [
The reliability behavior of flight control system and its components can be represented
in form of discrete-continuous stochastic system [
It was taken into account that all FCS components (elements) failures are independent and they are considered as critical failures (CF) if they result in complete or partial loss of the system performance. In addition, it was assumed that durations of all procedures in research objects are random variables having an exponential distribution, and a number of events on the observation interval is defined by the Poisson distribution. 3.1
Improved Reliability
Model for Fault-Tolerant Unit with Bimodal
Parallel/Series Redundancy Reliability models for each of three FTUs with bimodal parallel/series redundancy for gyroscopes and accelerometers for the 2nd navigation subsystem variant (discussed in Section 2), consist of two separate blocks. These blocks are gyroscopes unit and accelerometers unit with simple parallel redundancy (Fig. 2). Such approach allows initial building improved reliability model for FTU with simple parallel redundancy and on its basis forming mathematical model for FTU with bimodal parallel/series redundancy.
On the first stage, according to the methods presented in [
Detection device continuously controls the ME state and does not control the SE operability. Detection procedure has two alternative completions:
successful – detection device defines the ME failure and transfers a signal to switching equipment with probability PD;
failed (the 2nd type of control method errors) – detection device does not distinguish the ME failure with probability (1 – PD).
Detection device can give out a false alarm, which is classified as the 1st type of control method errors. In this case, detection device mistakes operating ME for failed with probability PFA. False alarm rate λFA is defined as 1/TFA, where TFA – mean time, when false alarm signal can be sent out from detection device with probability PFA = 1.
If detection procedure is successful or in case of false alarm, the detection device will transfer a signal to switching device to start switching procedure. This procedure has four completion alternatives:
1) successful ME unhooking and hooking of operating or failed SE with probability PS; 2) successful ME unhooking and failed SE hooking with probability PDN; 3) failed ME unhooking and SE hooking with probability PNN; 4) “opposing connection” with probability PNC. Probability of successful switching procedure completion is determined from the formula: where (PDN + PNC + PNN ) – probability of failed switching procedure completion.
Probability of successful procedure completion for ME isolation in case of its failure or false alarm is determined from the formula:
PS = 1− (PDN + PNC + PNN ),
PSI = 1− PNC . (1) (2)
The developed Markov model for fault-tolerant unit with simple parallel redundancy is shown in Fig. 3.
Mathematical reliability model for considered FTU is presented in form of differential Chapman – Kolmogorov equations set: dP1(t) / dt = −(M + R + FA )P1(t) dP6 (t) / dt = FA PNN P3 (t) + R P4 (t) − M P6 (t) dP2 (t) / dt = (M PD PS + FA PS )P1(t) − (M + FA (1 − PS + PD ))P2 (t) + M PD PS P4 (t) ...
where Pі ( t ) is probability of system being in State i (i 1 ..., 7) at time t. State 7 corresponds to CF state in Fig. 3.
Here and in other stated below mathematical models, the equitations for critical failure states were replaced by the normalization requirement. (3) 3.2
Improved Reliability Model for Fault-Tolerant Unit with Series/Parallel Redundancy Bimodal Reliability block diagram of fault-tolerant unit with bimodal series/parallel redundancy (gyroscopes and accelerometers unit) is depicted in Fig. 4.
Reliability model of such unit with active redundancy consists of two blocks: main block – two different-type main elements (ME1 and ME2) in series, and standby block – two standby elements (SE1 and SE2) in series. Two separate detection devices (DD1 and DD2) control respectively ME1 and ME2 operability and do not control the state of standby elements. Detection procedure for each main elements has two alternative completions:
successful – detection device DD1 or DD2 defines the main elements failure and transfers a signal to switching equipment with probabilitis PD1 and PD2;
where Pі ( t ) is probability of system being in State i (i 1 ..., 21) at time t. State 21 corresponds to CF state in Fig. 5. To achieve continuous performance of control unit and accordingly autopilot, the three-component active redundancy for this component was considered. This FTU includes main element, two standby elements (SE1 and SE2) in parallel and suitable detection and switching devices. Its fault-tolerant design enables the unit to continue operation with gradual reliability reducing after failure of main and two standby elements, which take ME position.
The reliability model is represented by reliability parameters (λM1, λR = λR1 = λR2) and DSD effectiveness parameters (PD1, PD2, λFA1, λFA2, PS, PDN, PNC and PNN). The Markov model for fault-tolerant unit with three-component redundancy is shown in Fig. 6.
Mathematical reliability model for the considered FTU is presented in form of differential Chapman – Kolmogorov equations set: dP1(t) / dt = −(M + R + FA )P1(t) dP2 (t) / dt = −(M PD PS + FA PD )P1(t) − (M + R + FA )P2 (t) + M PD PS P4 (t) ... (5) where Pі ( t ) is probability of system being in State i (i 1 ..., 13) at time t. State 13 corresponds to CF state in Fig. 6. 3.4
Improved Reliability Model for Fault-Tolerant Flight Computer The 2nd flight computer variant, presented in Section 2, was investigated in this paper. Its block-diagram is depicted in Fig. 7, where three MPs in majority voting structure core (MP1, MP2, MP3) and one MPR in standby mode, VU –voting unit, FD – fault detector and KF- 2 – Kalman filter.
MP1 MP2 MP3 MPR
FD
VU
KF-2 Fig. 7. Block diagram of flight computer with majority-voting redundancy 2-out-of-3 microprocessors and inherent standby microprocessor
Fault detector provides failure detection of MVS core microprocessors. It compares MP’s (MP1, MP2, and MP3) out signals and KF- 2 input signal. If these signals are not identical, FD transfers a signal about failure of the certain MP and a command to the idle MPR to switch to corresponding VU input.
The MP software failure rate is much higher than the MP hardware failure rate [
The Kalman filter KF-2 performs linear quadratic estimation of system state, thus its reliability is much higher, than for other components. The problem of providing its fault-tolerance was not considered in the paper.
The results of reliability model development for the 2nd flight computer variant: 1) the Markov model on the ground of basic events (Fig. 8); 2) mathematical reliability model in form of differential Chapman – Kolmogorov equations set: dP1(t) / dt = −(4MP + 3 FA + VU )P1(t) dP2 (t) / dt = (MP (1 − PD + PD (PDN + PNN ) + FA PDN ))P1(t) − − (MP (2PD PS + 3 − 2PS ) + 2FA + VU )P2 (t) + + (MP (1 − PD + PD (PDN + PNN ) + FA PDN ))P9 (t) ... dP40(t) / dt = FA PNN P31(t) + FA PNN P32(t) + FA PNN P33(t) − (3MP + VU )P40(t)
where Pі ( t ) is probability of system being in State i (i 1 ..., 41) at time t.
State 41 corresponds to CF state in Fig. 8.
(6)
Using certain input data, we calculated reliability of FCS components. The reliability
estimation results, presented in Tables 1, 2 and 3 and Fig. 9, confirm the known thesis
that non-perfect detection and switching devices (in comparison with perfect
equipment) decrease system reliability [
variants 1st 2nd 3rd
Detection and switching devices
– perfect non-perfect perfect non-perfect Detection and switching devices
– perfect non-perfect perfect non-perfect
The considerable difference in UAV reliability results, obtained with the wellknown and improved models (Table 4), indicates a significant overall impact of DSD effectiveness on the unmanned aerial vehicle reliability. The less effective detection and switching devices cause the bigger mentioned discrepancy. Consequently, it results in the considerable lowering of UAV employment effectiveness, including its flight duration and regularity of operations.
The achieved results certainty is validated by use of well-proven mathematical tools
as well as reaching asymptotic agreement with results that were attained with
application of the known models (Table 5). The obtained results have clear physical
interpretation and do not contradict the well-known scientific theories.
Rationale for expedient fault-tolerant configurations of FCS components is provided
in the frame of flight control system reliability synthesis. The proposed synthesis
technique [
The improved FTU reliability models with the higher degree of adequacy comparatively to the well-known models determine the technique originality. Using of these models enables increasing certainty of reliability synthesis results.
One of the primary outcomes of application of the offered synthesis technique is forming up the sets of the rational fault-tolerant configurations of FCS components considering maintenance and repair modes. These sets appear as input data to solve optimization problem for FCS structure composition. 4
A key FCS design task is to realize the required field reliability level and ensure UAV
effectiveness with necessary flight duration and regularity of operations, and save
resources in achieving this objective [
To complete the foregoing tasks and solve this multi-objective design problem, the
resultant criteria method was applied [
Zkij = 1 Skij + 2 Mkij (7) where 1 2 – weight coefficients for setting a balance expenditure state between 1 kW power consumption and 1 kg of equipment weight;
indexes – i 1 ..., r; for navigation subsystem – k=1; j 1 ..., n1і; flight computer – k=2; j 1 ..., n2і; autopilot – k=3; j 1 ..., n3і;
M kij and Skij – weight and power consumption for realization of fault-tolerant configuration j for FCS component k considering MRM i.
Accordingly, the optimization criterion is a minimum expenditure of technical resources that defined from the formula:
k Zi = min Zkij (8)
i=1
Since the reliability is the basis for making optimum design decision, the sets of the rational fault-tolerant configurations of FCS components with considering MRMs are the main input data for solving optimization problem and primary optimization constraint.
Thus, for each maintenance and repair mode i (i 1 ..., r), which is determined by the operation interval TOPi (Table 6), can be formed three sets of rational fault-tolerant configurations for each of three FCS components accordingly: for navigation subsystem – N1і (1,…, n1і); flight computer – N2і (1,…, n2і); autopilot – N3і (1,…, n3і).
In addition to reliability parameters, the normalized values of UAV flight duration
and regularity of operations, and flight control system weight, power consumption
and overall cost are defined as optimization constraints. The estimation of overall cost
for FCS components is made on basis of analysis their cost of design, engineering,
and procurement, as well as operating and support costs [
As an example, the offered optimization technique was used for UAV flight control system design with selection of rational MRM from three basic maintenance and repair modes. It is considered that maintenance personnel should be used to restore the system operation: for the 1st MRM – after every UAV flight, and for the 2nd and 3rd modes – correspondingly after intermaintenance and overhaul period completion. The technique application allows choosing the expedient MRM that enables increasing mobility of unmanned aircraft system sections and declining requirements to qualification of maintenance specialists due to the grounded integration of FCS components with high reliability going from redundancy addition.
Based on the analysis of the optimization problem outcomes using the well-known
and offered reliability models, it was concluded, that applying the well-known models
determines making inefficient design decisions. It results in reduction of redundancy
amount, and selection of less reliable elements. As experience has shown, it is
practically one of main causes for development of technical systems with the field
reliability level 10-15 % lower than was measured during design [
Conclusions 1. The proposed reliability-oriented approach for UAV flight control system structural optimization enables increasing results certainty owing to improved reliability models for the system fault-tolerant configurations with high adequacy level.
2. The developed optimization technique ensures increasing non-failure UAV operating time with technical resources minimization for FCS design, meeting required system reliability level, flight duration and regularity of operations, observing principal constraints (weight, power consumption and overall cost), taking different maintenance modes into consideration.