Technique of synthesis of the suitable program of diagnosing of the onboard equipment of the spacecraft on reliability taking into account precision characteristics of measuring instruments Текст научной статьи по специальности «Компьютерные и информационные науки»

Е ТЕХНОЛОГИИ В КОСМИЧЕСКИХ ИССЛЕДОВАНИЯХ ЗЕМЛИ, Т 11 № 3-2019 ии на английском языке: авиационная и ракетно-космическая техника

doi: 10.24411/2409-5419-2018-10273

TECHNIQUE OF SYNTHESIS OF THE SUITABLE PROGRAM OF DIAGNOSING OF THE ONBOARD EQUIPMENT OF THE SPACECRAFT ON RELIABILITY TAKING INTO ACCOUNT PRECISION CHARACTERISTICS OF MEASURING INSTRUMENTS

EKATERINA A. ZAHAROVA1

ANATOLIY D. KHOMONENKO2

ANATOLIY M. BARANOVSKY3

Information about authors:

1postgraduate student of the of Military Space Academy, St-Petersburg, Russia, [email protected];

2PhD, Full Professor, Head of the Department of Information and Computing systems of Emperor Alexander I St. Petersburg state transport university, Professor of the of Military Space Academy, St-Petersburg, Russia, [email protected]

ABSTRACT

The modern spacecraft's are difficult subjects to control and diagnosing which at completions and partial modernization allow joint operation of the elements having various volume of statistical information on defects and refusals, and at times and total absence of this information. When diagnosing the onboard equipment of spacecraft the problem of reliability of decision-making is particularly acute very. The poor quality of diagnosing can lead to adoption of wrong solutions of the technical condition and is negative influence processes of maintenance of a subject to diagnosing that leads to decrease in efficiency of the solution of tasks, or to start of spacecraft with faulty onboard equipment of that means failure of the set target task. It demands further intensive development of new approaches to determination of technical condition on the basis of diverse prior and current information as the existing approaches not rather fully reflect the proceeding processes in an object and the system of diagnosing. In this regard the technique of synthesis of the suitable program of diagnosing of the onboard equipment of the spacecraft on reliability on the basis of the hidden Markov models based on Bayesian networks of trust is developed. Application of Bayesian networks of trust in models of diagnosing allows to increase reliability of results of diagnosing at the expense of a possibility of accounting of uncertainty of results of measurements of diagnostic signs, dynamics of prior information on technical condition of a subject to diagnosing, coverage of considerable volume of diagnostic signs and also uses of parameters of the law of distribution of values of diagnostic signs and precision characteristics of measuring instruments. Use of the office of Bayesian networks of trust significantly supplements models and methods of the solution of problems of technical diagnostics. The example of synthesis of the suitable program of diagnosing of a control system of the movement of the spacecraft on reliability is presented. According to authors, results of researches can be of interest to developers of control devices and tests of the onboard equipment of spacecraft's both by preparation of spacecraft for start, and in flight.

3PhD, Docent, Professor of the of Military Space Academy, St-Petersburg, Russia, [email protected]

KEYWORDS: diagnosing; onboard equipment; technical condition; Bayesian network of trust; precision characteristics, posteriori conclusion.

For citation: Zaharova E. A., Khomonenko A. D., Baranovsky A. M. Technique of synthesis of the suitable program of diagnosing of the onboard equipment of the spacecraft on reliability taking into account precision characteristics of measuring instruments. H&ES Research. 2019. Vol. 11. No. 3. Pp. 100-108. doi: 10.24411/2409-5419-2018-10273

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ESEARC-

Introduction

Increase in complexity of the modern missile and space equipment is followed by increase in requirements to efficiency of its regular functioning [1]. Considerably processes of determination of technical condition of systems at ground tests became complicated and in you weed that complicates prevention and parrying of refusals in various modes of functioning. timely detection of malfunctions and refusals. The most important component of the spacecraft (S) is the control system of the movement (CSM) which provides, in particular, management of the angular movement for the purpose of high-quality working off of the program of management during the operation of the special equipment. In this regard it is necessary to carry out reliable diagnosing of CSM of S as on the technical complex (TC) that there was no start of S with disabled CSM, and further during flight that there was no failure of performance of a target task because of refusal of CSM of S [2-3].

Problem definition. The problem of ensuring the required reliability of diagnosing of CSM of S as subject to diagnosing on shopping mall is formulated as follows [4].

The formalized models of a subject to diagnosing Mod, process of diagnosing Mpd and model of measuring instruments

of sensors are set M.:

d

M = <S, Pr, A>,

Od 7 7 7

M = <Y,, Y , n, Q, A , B , T*(ty>,

pd d7 n 7 7 7 pr pr v 0' '

Md = <Sr AS, BS, ^ where

- S = (5,. | i = 0, m} — set of types of technical conditions of BO S; _

- Pr = (p^ | j = 1, n} — the set of the diagnostic signs

(DS) consisting of the discrete DP Prd = {prdj. | j = 1, l} and continuous DP Prn = {prnj. | j = 1, h} described by the normal law of distribution with parameters m. and c.;

- A = {Xi | i = 1, m} — set of intensities of failures of equipment packages of an object;

- Yd = {ydj | j = 1, l} — set of the received signals from sensors of discrete type and Yn = {ynj | j = 1, h} — a set of the received signals from sensors of continuous type;

- n = (rnj | j = 1, n} — a set of checks of DP for which are set T = (xj | j = 1, n} — duration of checks, Apr = {«prj 1 J =1, n} and Bpr = (pprj | j = in} — probabilities of methodical errors (the 1st and 2nd sort) which are caused by errors of purpose of admissions to the measured parameters;

- W = {Rw| w = 0,..., (2m+1-l)} — the event algebra W, W = 2m+1-1 set on a set S in which elements ft , ={S„, S } —

max m+1 v 0 mJ

are the information statuses of process of diagnosing which are formed as the result of the carried-out inspections;

- T*(t0) = [t0,+ro) — time point, where t0 — initial time point of operation of a system, and t0 + xd — corresponds to diagnosing time;

- Sr = [Srj \j = 1,n} — a set of the sensors fixing values of diagnostic signs for which metrological characteristics

are set. For sensors of discrete type are set ASr = (aSr j | j = 1, l}

and BSr = (PSrj | j = 1, l} — sets of error probabilities of checks

(the 1st and 2nd sort), for sensors of continuous type measurement uncertainty distribution functions in the form of the

normal law aSr = (aSrj | j = 1, h}, facility instrumentations

caused by errors, are set by noises and other negative factors. It is required: synthesize the diagnostic program

Prog* = {p

7(1)'

j(cy

■••, Py «},

where {p

j(i)'

, p pj(„,)} — an ordered set (structure and

the sequence) of checks, j — a code name of check c — sequence number of check, such that

D (Pr og * )= Z [^(^ / yj),.^ („•) j_kj)-PiSi)] > Dzad

i=0,m j =1,n

provided that T(Prog*) < Tdop, Tdop — an allowed time of diagnosing.

Assumptions: 1) the value of each diagnostic sign is measured by one sensor; 2) at the same time there can be only one failure; 3) the observability of types of the CU is provided.

Task solution. For synthesis of the diagnostic program hidden Markov models on the basis of the Bayesian networks of trust (BNT) representing the probabilistic and graphic models having the following advantages [5] are used:

1. High performance of a solution of tasks for complex systems in which there are a lot of observed signs of variables

Yj, {yj 1 j = 1 ^ , n < 1000 allowing decomposition on continuous and discrete diagnostic signs.

2. Accounting of receipt of new information — certificates (new data on results of checks of diagnostic signs Y(t) or information on degrees of product availability P(S)).

The data provided in problem definition are necessary for synthesis of the diagnostic program OE S, suitable on reliability, on the basis of Bayesian networks of trust including: failure density, given about diagnostic signs, given about precision characteristics of measuring instruments of DP.

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НАУКОЕМКИЕ ТЕХНОЛОГИИ В КОСМИЧЕСКИХ ИССЛЕДОВАНИЯХ ЗЕМЛИ, Т 11 № 3-2019 публикации на английском языке: авиационная и ракетно-космическая техника

The technique of synthesis represents the following sequence of actions:

Step 1. Construct a diagnosing process model in the form of a hidden Markov model on the basis of the Bayesian network of trust (BNT):

Step 1.1. Give a task topology of a Bayesian network of trust — to define prichinno investigative communications proceeding from structure of a system [10].

Step 1.2. Calculate the prior probabilities of types of the CU [P(Si | i = 0m} :

Step 2.3. If the measured value DP {< ynj >, j = 1, h} is continuous, then to define reliability for this check. Reliability are the values of conditional probabilities of types

of technical states (Si),i = 0,mj, average on a priori probabilities of technical condition, from results of checks |p(Sj /ynj j,j = 0,m;j = 1,. The reliability of check is defined by expression [7-8]:

PCS«,) = -

1

1

1 - e

D({n,}) = -

Z f [ynj tpnj)-f ([ /S)• p(st)

j

mm) z m f (ynj iprn,)• f (j /s)• p(s)

(i)

1 - e"

xP(S, ) = -

Z Z P(S./ynj)• P(S,)

P(Si ) =

ml -h

1 m 1 - e 1

i=! e

j

Step 1.3. Specify the prior information for DP

Kr j I J = 1, n} and {Ppr j \ j = l, n}.

Step 1.4. Set observation model, i.e. conditional prob- D({%j}) =

abilities of DP set in the CU {P(prj / St) | i = 0m; j = In},

using, including, parameters of the distribution law of discrete and continuous diagnostic signs with parameters and a.. xP(St) = -

Step 1.5. Specify the prior information for the sensor of E P(Si) i=°'mJ=v

^ p(g ) i-0,m j—l,h

i

Step 2.4. Ifthe measuredvalue is discrete{<ydj >, j = 1,l}, then to define reliability for this check. The reliability of check is defined by expression:

E.P( /vrdjj )■ P( /S)• P(Si)

m / x

EPS) m E p(ydj /prdj)■ p(j/S)■ P(S)

i=0,m j=l,l

m e p(Si/yd,)■p(si)

discrete type (aSr j | j = 1, l} and (aSr. | j = 1, l} — error probabilities of checks (the 1st and 2nd sort), and for the sensor of continuous type to set metrological characteristics in the form of the normal distribution law of page {aSrj | j = 1, h}.

Step 1.6. Set the model of measurements i.e. conditional probabilities connecting metrological characteristics of measuring instruments and the DP [6] model values {P(Srj /prj)\j = \n}.

Step 2. Synthesize the diagnostic program, suitable on reliability, on the basis of a posteriori output of Bayesian networks of trust:

Step 2.1. With the initial uncertainty of information state R-m+i ={S0, Sp..., Sm} to carry out the distribution of model results of checks in the BNT {< yj >, j = 1, n}. Distribution of model results of checks to BNT is understood as addition of the evidence of the DP model value and recalculation of probabilities of the CU.

Step 2.2. To find possible information (intermediate) states Rw(ra = 0, 1,., m, (2m+1-1)), which are formed as the result of the carried-out inspections on the basis of the DP model values.

Step 2.5. To find for again formed information states, checks which provide discernability of the CU and to carry out distribution of possible results of checks to BNT for the purpose of finding of new possible intermediate states.

Step 2.6. The previous step repeats until all information states do not consist of the only degree of product availability — Ri = {Si, i=0m}.

Step 2.7. To calculate aW) = ^ [P(S./yda),...,y„(„,)X+,J(1)+...+Tj(n,) P(si)].

i = 0, m j = 1, l

Step 2.8. To find T (Prog*) = £ xj.

j=

Step 2.9. To check a condition D(Prog*) > Dzad, to check T(Prog*) < rdop.

Step 2.10. If the condition of a step 2.9 is not satisfied, then to create the DP set with other characteristics.

Let's give an example of the solution of a problem of synthesis suitable on reliability.

X, t

X.. t

e

h t

x, t

e

ill

ESEARC-

Act as prior information the failure rate of blocks CSM of S—l which are given in table 1.

As types of the CU (tab. 2) we will define one efficient S0 and 7 disabled Si (i = 1,7), called by single refusals corresponding blocks presented in table 2.

The values of probabilities of technical states calculated on a formula (1) for time td are presented in table 3.

Values of continuous diagnostic signs pr1 — temperatures, pr2 — tension of onboard sensors, pr3 — load current and discrete diagnostic signs — pr4, pr5, pr6, pr7, accepting binary

Table 1

Structure and failure rate of blocks CSM of S

The name of the equipment Intensity of refusal — l

1. Measuring instrument of an angular position l

2. Determinant of coordinates of stars l

3. Measuring instrument of angular speed l

4. Plotter of a local vertical l

5. Power gyroscopic complex l

6. System of measurement of increment of speed l

7. Coordination device block l

Table 2

Types of technical conditions of the onboard equipment CSM of S

S0 — efficient S4 — failure of the plotter of a local vertical

S1 — failure of the measuring instrument of an angular position S5 — refusal of a power gyroscopic complex

S2 — refusal of determinant of coordinates of stars S6 — failure of the system of measurement of increment of speed

S3 — failure of the measuring instrument of angular speed S7 — failure of the block of the device of coordination

Table 3

Probabilities of technical states CSM of S

Probabilities of the CU Type of the CU Probabilities of the CU Type of the CU

P(S0) =0.754 efficient P(S4)=0.038 failure of the plotter of a local vertical

P(S1) =0.096 failure of the measuring instrument of an angular position of P(S5)=0.019 refusal of a power gyroscopic complex

P(S2) =0.012 refusal of determinant of coordinates of stars P(S6)=2.484*10-3 failure of the system of measurement of increment of speed

P(S3) =0.076 failure of the measuring instrument of angular speed of P(S7)=2.417*10-3 failure of the block of the device of coordination

НАУКОЕМКИЕ ТЕХНОЛОГИИ В КОСМИЧЕСКИХ ИССЛЕДОВАНИЯХ ЗЕМЛИ, Т 11 № 3-2019 публикации на английском языке: авиационная и ракетно-космическая техника

values {0,1}, are presented in table 4. The set error probabilities of the first and second sort DP are presented in table 5.

For accounting of precision characteristics of measuring instrumentstheobservationmodelisset {P(Srj / prj )| j = 1, n},

Table 4

DP model values CSM of S

Table 5

Errors 1 and 2 sorts DP

Check for discrete DP

a ß

P1^ P1^ P^ Pr7 О.О1 О.О5

in statements of the problem we will accept set the characteristics of measuring instruments presented in table 6.

The Bayesian network of trust [8] operates with unconditional and conditional probabilities. Processing of conditional probabilities of DP for BNT is given in table 7.

Characteristics of measuring instruments for sensors of continuous type are set in the form of family of functions of density of probability of the normal law of distribution by means of parameter ^Sr. The block considering precision characteristics of measuring instruments, being the block of continuous type (continuos) into which the set passport values of tool errors are entered [9] is entered into model of process of diagnosing of OE of S in BNT.

Data for creation of Bayesian network are the probabilities of types of technical states determined by formulas (1) (tab. 3), model values of diagnostic signs (tab. 4, 5, 7), characteristics of the measuring instruments (tab. 6) set by discrete and continuous sizes.

Table 6

Characteristics of measuring instruments of discrete and continuous values

pr;

S. 1 prP °С pr2,V Pr3, А binary DP

Pr4 Pr5 Pr6 Pr7

S* [5; 25] [18;22] [1.1;3.О5] О О О О

S1 [5; 25] [22;33] [1.1; 3.О5] О О О 1

S2 [25;45] [18;22] [3.О5; 5] О О О О

S3 [25;45] [22;33] [3.О5; 5] О О О О

S4 [25;45] [22;33] [1.1; 3.О5] О О О О

S5 [5; 25] [22;33] [1.1; 3.О5] 1 О О О

S6 [5; 25] [22;33] [1.1; 3.О5] О 1 О О

S7 [5; 25] [22;33] [1.1; 3.О5] 1 О 1 О

Duration of the check, min For sensors of the signal Duration of the check, min For sensors of continuous type

aSr ; ßsr ; CTSr ;

П4 2 n1 4 О О.О3

П5 4 О.О6 О.ОО1

п6 4 П2 5 О О.О5

П7 2 П3 3 О О.О4

Table 7

Error handling of the first and second sort DP for BNT

P(prd4 /{So,Si,S2,S3,S4,S6}) = l-±4 = 0.99 P(prd5 Z {So,Si,S2,S3,SA,S5,S7}) = l-±5 = 0.99

P(prd4 / {S5,S7}) = 2 4 = 0.05 P(prd5 / {56}) =2 5 = 0.05

P( / {^5, S7}) = 1 - 2 4 = 0.95 P( Pd 5 / S ,Si ,S2 S ,S4, S5 ,S7}) = ±5 = 0.01

P( Z {So, Si ,S2 ,S3 ,S4 ,S6}) = ±4 = 0.01 P( Z {56}) = 1 -2 5 = 0.95

D(p2) = -

• [P(So/ yn2) • P(Sq)-

At initial uncertainty of technical states S = (S; \i = 0,m} it is necessary to calculate reliability of all checks (as all checks are admissible) taking into account precision characteristics of measuring instruments and to define the check having the maximum reliability. On the subsequent steps, some checks will be inadmissible or need for them will be absent, therefore, the set of alternatives of checks will be narrowed, time of checks and volume of calculations is reduced.

In fig. 1 the fragment of process of diagnosing of a system at which on the 1st step there is a check p2 is represented.

At receipt of the certificate < yn2 > there is a narrowing of area of uncertainty of types of technical states to {S1, S3 S4 S5 S6 S7}, and at receipt < yn2 > - {S0, S2}. Therefore, the average reliability of check p 2 will be equal:

I PS)

i-0

+p(Si / y„2) ■ p( Sr)+p( S2 / yn2) ■ P(S2)+ +P(S3 / yn2) ■ P(S3) + P(S4 / yn2 ) ■ P(S4 ) + +(P(S5 /yn2)■ P(S5) + P(S6 /yn2)■ P(S6) +P(S7/ yn2) ■ P(S7)]

In fig. 2 probabilities of types of technical states in the absence of certificates are presented and at receipt of certificates after conducting check p 2 at the time of t = 60 min.

j J »? - ' . S-j ^

Fig. 1. Fragment of process of diagnosing consisting of check n2

D(p2) = ~

1

• [ P(Vyn2) • P(So) +

Z PS)

i=0

+P(Si / yn2) • P(Si) + P(S2 / yn2) • P(S2) + +P(S3 / yn2 ) • P(S3 ) + P(S4 / yn2 ) • P(S4 ) + + (P(S5 / yn2 ) • P(S5 ) + P(S6 / yn2 ) • P(S6 ) + +P(S7 / yn2) • P(S7)] = 0.8654 • 0,754 + +0.0998 • 0.096 + 0.0138 • 0.012 + 0.0790 • 0.076 + +0.0395 • 0.038 + 0.0197 • 0.019 + 0.003 • 0.0002484 + +0.003 • 0.002417 = 0.67;

By analogy the others are found reliability of checks [14-15]. As a result of performance of the sequence of steps of

1

ä-QUi

i i

22.73 Mean 36.0CJ Variance

21.73 Mean 11.09 Variance

75.74 State Ü 9.64 State 1 1.21 State 2 7.63 State 3 3.82 State 4 1.91 StateB Ü.02 State 6 Ü.02 State 7

$ 4 JO D2

7 ('JO F'r2

On ?

22X10 Mean 0,00 Variance

20.83 Mean 5.52 Variance

66.54 State 0 5.05 State 1 1.38 State 2 4.00 State 3 2.00 State 4 1.00 State 5

0.01 State 6

0.01 State 7

$ 1JDD2 $ QD Pr2

L

b

Fig. 2. Probabilities of technical states: a — in the absence of certificates; b — at receipt of the certificate; c — at receipt of the certificate

25.00 Mean 0.00 Variance

21.74 Mean 9,97 Variance

74.96 State 0

9.95 State 1

1.19 State 2

7,90 State 3

3,95 State 4

1,97 State 5

0,03 State 6

0,03 State 7

a

c

НАУКОЕМКИЕ ТЕХНОЛОГИИ В КОСМИЧЕСКИХ ИССЛЕДОВАНИЯХ ЗЕМЛИ, Т 11 № 3-2019 публикации на английском языке: авиационная и ракетно-космическая техника

Fig. 3. Programs of diagnosing CSM of S for time point td = 60 min: a — the program of diagnosing CSM of S without dostovernost of checks; b — the program of diagnosing CSM of S taking into account dostovernost of checks

b

a

a technique, the suitable program of diagnosing on reliability for timepoint of diagnosing of td = 60 min. presented in fig. 3 is constructed.

For CSM of S average reliability unconditional (Db) and the suitable program (D(Prog )) are equal respectively [7-8]:

Db = 0.843;

D(Prog* ) = (P (S0 / yd6, yd5, Уn3, yd4, Уn1, yd7 ) • P (S0 ) +

+ P (( yd 6, yd 5' yd 3, yd 4, Уn2, yd 7 )• P (S1 ))X

•. • +..(P(S0S1 / yd6, yd5, yn3 , yd4, yn1 ) • P(S0S1 ) +

+ P (S5 / Уd6, Уd5, Уd3, Уd4, yn2 )P (S5 )). + ...

+...(P (S7/ yd6 )• P (S7 )) = 0.956.

As a result of comparison of dostovernost we promote reliability for 14% at implementation of the program of diagnosing taking into account dostovernost of checks.

Conclusion. Accounting of precision characteristics of measuring instruments increases adequacy of model of process of diagnosing, at the set requirements in TTZ of reliability of results of diagnosing. The unconditional program of diagnosing

CSM of S (without dostovernost of checks) does not meet the established requirements D(Prog) = 0.843 < 0.95, and the program of diagnosing CSM of S taking mto account dostovernost of checks meets requirements of TZ ^(Prog ) = 0.956 > 0.95. The received results give the chance to the automated probing system at ground tests of the onboard equipment of the spacecraft on a technical complex quickly to synthesize programs of diagnosing in case of refusal. Further results of researches can be directed to creation of programs of diagnosing taking into account dynamics of technical condition.

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НАУКОЕМКИЕ ТЕХНОЛОГИИ В КОСМИЧЕСКИХ ИССЛЕДОВАНИЯХ ЗЕМЛИ, Т ПИ

бликации на английском языке: авиационная и ракетно-космическая техника

МЕТОДИКА СИНТЕЗА ПРИГОДНОМ ПО ДОСТОВЕРНОСТИ ПРОГРАММЫ ДИАГНОСТИРОВАНИЯ БОРТОВОГО ОБОРУДОВАНИЯ КОСМИЧЕСКОГО АППАРАТА С УЧЕТОМ ТОЧНОСТНЫХ ХАРАКТЕРИСТИК СРЕДСТВ ИЗМЕРЕНИЙ

ЗАХАРОВА Екатерина Алексеевна, KEYWORDS: диагностирование; бортовое оборудование; техни-

г. Санкт-Петербург, Россия, [email protected] ческое состояние; байесовская сеть доверия; точностные харак-

теристики, апостериорный вывод.

ХОМОНЕНКО Анатолий Дмитриевич,

г. Санкт-Петербург, Россия, [email protected]

БАРАНОВСКИЙ Анатолий Михайлович,

г. Санкт-Петербург, Россия, [email protected]

АННОТАЦИЯ

Современные космические аппараты представляют собой сложные объекты контроля и диагностирования, которые при доработках и частичной модернизации допускают совместную эксплуатацию элементов, имеющих различный объем статистической информации о дефектах и отказах, а порой и полное отсутствие данной информации. При диагностировании бортового оборудования космических аппаратов проблема достоверности принятия решения стоит весьма остро. Низкое качество диагностирования может привести к принятию ошибочных решений технического состояния и негативно повлиять на процессы восстановления работоспособности объекта диагностирования, что приводит к снижению оперативности решения задач, либо к запуску космических аппаратов с неисправным бортовым оборудованием, что означает срыв поставленной целевой задачи. Это требует дальнейшего интенсивного развития новых подходов к определению технического состояния на основе разнородной априорной и текущей информации, так как существующие подходы не достаточно полно отражают протекающие процессы в объекте и системе диагностирования. В связи с этим разработана методика синтеза пригодной по достоверности программы диагностирования бортового оборудования космического аппарата на основе скрытых марковских моделей, основанная на байесовских сетях доверия. Применение байесовских сетей доверия в моделях диагностирования позволяет повысить достоверность результатов диагностирова-

ния за счет возможности учета неопределенности результатов измерений диагностических признаков, динамики априорной информации о техническом состоянии объекта диагностирования, охвата значительного объема диагностических признаков, а также использования параметров закона распределения значений диагностических признаков и точностных характеристик средств измерений. Применение аппарата байесовских сетей доверия существенно дополняет модели и методы решения задач технической диагностики. Представлен пример синтеза пригодной по достоверности программы диагностирования системы управления движением космического аппарата. По мнению авторов, результаты исследований могут представлять интерес для разработчиков средств контроля и испытаний бортового оборудования космических аппаратов как при подготовке космических аппаратовк запуску, так и в полете.

СВЕДЕНИЯ ОБ АВТОРАХ:

Захарова Е.А., адъюнкт Военно-космической академии имени А.Ф. Можайского;

Хомоненко А.Д., д.т.н, заведующий кафедрой информационные и вычислительные системы Петербургского государственного университета путей сообщения Императора Александра I, профессор Военно-космической академии имени А.Ф. Можайского; Барановский А.М., к.т.н, профессор Военно-космической академии имени А.Ф. Можайского.

Для цитирования: Захарова Е.А., Хомоненко А.Д., Барановский А. М. Методика синтеза пригодной по достоверности программы диагностирования бортового оборудования космического аппарата с учетом точностных характеристик средств измерений // Наукоемкие технологии в космических исследованиях Земли. 2019. Т. 11. № 3. С. 100-108. Сои 10.24411/2409-5419-2018-10273