Multiset Analysis of Consequences of Natural Disasters Impacts on Large-Scale Industrial Systems

Abstract

Financial University under the Government of Russian Federation, Moscow, Russian Federation, RU sheremet@rfbr.ru Paper is dedicated to the new approach to distributed industrial systems (IS) sustainability/ vulnerability assessment. This approach is based on the unitary multiset grammars (UMG) as a flexible and convenient tool designed specially for large systems analysis and optimization. UMG description of IS technological base as well as multiset representation of order completed by the IS, its resource base and impact on the IS are presented. Criterion for recognition of IS sustainability to the impact is formulated. UMG extension for natural disasters impacts (NDI) representation is introduced, and criterion for recognition of IS sustainability to the NDI is also presented. The solution of the reverse problem, concerning part of the order, which may be completed by the affected IS, is described. Implementation issues are considered.

Multiset-Based Assessment of Resilience of Sociotechnological Systems to Natural Hazards

“…List is interpreted as multiset, i.e., n 1 Á a 1 ; …; n m Á a m fg . The so-called structural and technological interpretations of unitary rules are used in the IS resilience assessment [2].…”

“…where UR a ! n 1 Á a 1 , …,n m Á a m for unambiguity is represented in the angle brackets, and þ, À , * are symbols of operations on multisets (addition, subtraction of multisets, and multiplication of constant on multiset, respectively) [1,2,12,13].…”

“…As it was shown in [1,2], multiset-based approach to such assessment is one of the most suitable perspectives from both descriptional and computational points of view. The core of this approach is representation of technological base of the industrial systems (IS), producing necessary resources, by special multiset grammar (MG), and its resource base (RB)-by multiset (MS).…”

On the assessment of sustainability of distributed sociotechnical systems to natural disasters

“…The theory of recursive multisets (TRMS), which main content was presented in [Sheremet, 2010[Sheremet, , 2011[Sheremet, , 2018, is a result of an attempt to integration of the best features of classical optimization and modern knowledge engineering. Besides this abstract goal, there were also some practical aims, close to the listed DSTS-S design problems.…”

“…The impact on DSTS, whose technological base is represented by scheme of multigrammar =< 0 , >, may be easily represented by multiset Δ containing amounts of resources, eliminated from the resource base by this impact, and set Δ , gvishiani et al: sustainability of distributed dystems ES4004 containing destroyed devices. So, there is a quite simple and evident criterion for the assessment of DSTS sustainability to the impact < Δ , Δ > [Sheremet, 2016[Sheremet, , 2018: if (∃ ∈¯*)1 · ∈ where * =< 0 − Δ , − Δ >, then DSTS is sustainable to the impact (i.e., there exists at least one way of order completion by the affected system). The family of multiset grammars contains various classes of MG, describing various classes of DSTS and orders, while corresponding algorithms of generation of sets of multisets implement creation of schedules providing completion of those orders.…”