Description of approach to estimating survivability of complex structures under repeated impacts of high accuracy

Aim. The paper describes main concepts and definitions, survivability indices, methods used to estimate survivability in different external and internal conditions of application of technical systems, including the studies in the field of structural survivability obtained 30 years ago within the frames of the Soviet school of sciences. An attempt is made to overcome different technical understanding of survivability, which has been developed in the number of industries up to date – in ship industry, aviation, communication networks, energy, in defense industry. The question of succession between the properties of technical survivability and global system resilience is considered. Technical survivability is understood in two basic notions: а) as the system property to withstand negative external impacts (NI); b) as the system property to recover its operability after a failure or accident caused by external reasons. This paper considers the relation between the structural survivability when the system operability logic is binary, and is described by a logical function of operability, and the functional survivability when the operation of the system is described by the criterion of functional efficiency. Then the system failure is a decline in its efficiency below a preset value.

Methods. The technical system is considered as a controlled cybernetic system, which has specialized aids to ensure survivability (SAs). Logical and probabilistic methods and results of combinatorial theory of random placements are used in the analysis. It is supposed that: а) negative impacts (NI) are occasional and single-shot (one impact affects one element); b) each element of the system has binary logic (operability – failure) and zero resistance, i.e. it is for sure affected by one impact. Henceforth this assumption is generalized for the r-time NI and L- resistant elements. The paper also describes different variants of non-point models when the system part or the system as a whole are exposed to a group affection of the specialized type. The article also considers the variants of combination of reliability and survivability when failures due to internal and external reasons are analyzed simultaneously.

Results. Different variants of affection and functions of survivability of technical systems are reproduced. It has been educed that these distributions are based on simple and generalized Morgan numbers, as well as Stirling numbers of the second kind that can be reestablished on the basis of simplest recurrence relations. If the assumptions of a mathematical model are generalized in case of n the r-time NI and L-resistant elements, the generalized Morgan numbers used in the estimation of affection law are defined based on the theory of random placements, in the course of n-time differentiation of a generator polynomial. In this case it is not possible to set the recurrent relation between the generalized Morgan numbers. It is shown that under uniform assumptions in relation to a survivability model (equally resistant system elements, equally probable NI) in the core of relations for the function of survivability of the system, regardless of the affection law, there is a vector of structure redundancy F (u), where u is a number of affected elements, and F (u) is a number of operable states of the technical system with u failures.

Conclusions: point survivability models are a perfect tool to perform an express-analysis of structural complex systems and to obtain approximate estimates of survivability functions. Simplest assumptions of structural survivability can be generalized for the case when the logic of system operability is not binary, but is specified by the level of the system efficiency. In this case we should speak about functional survivability. PNP computational difficulty of the task of survivability estimation does not allow solving this task by means of a simple enumerating of states of the technical system and variants of NI. It is necessary to find the ways to avoid the complete search, as well by the conversion of the system operability function and its decomposition. survivability property should be designed and implemented into a technical system with consideration of how this property is ensured in biological and social systems.

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