An approach to forecasting damage due to unfavorable circumstances associated with indistinguishability of source data
Authors: Zolotukhin V. F. , Matershev A. V. , Podkolzina L. A. 
Published: December 2020

Introduction. When administering complex multi-parameter systems, management decisions are often made under uncertainty. There is an acute problem of reduction of the likelihood of unwanted events and mitigation of possible damage. The efficiency of predicting damage to complex systems depends directly on the quality of processing methods, systematization, and the amount of input data. It is required to improve methods for assessing and predicting damage and to develop new approaches and criteria for statistical forecasting of damage and evaluating the system reliability. The solution to such problems is complicated by a large number of indicators, data uncertainty, short series of observations, incomplete initial information, insufficiently developed scientific methodological apparatus. Existing methods for predicting damage in the systems of potentially dangerous objects do not take into account the causes of accidents that happened due to unfavorable circumstances. As a consequence, management decisions are made upon unreliable forecasting results. In this regard, an urgent scientific task is the development of methods and techniques for the formation of viable management decisions, free from this shortcoming. The major study objective is to consider a particular problem for predicting damage due to unfavorable circumstances associated with the indistinguishability of the initial data. The tasks are to consider this kind of uncertainty which includes indistinguishability of the true system condition and the real value of its quantitative characteristics; to formulate a combinatorial problem for the case when a rather dangerous composite feature is determined by the joint manifestation of two or more simple features.

Materials and Methods. Under the conditions of multiple indistinguishability, the following was used as the source data: a set of indistinguishable outcomes with reliable information on the event instance and the uncertainty of assigning the event to a certain type; a family of sets having the same number of elements. The Cartesian product of the families of the corresponding sets and the actual value of the group of a compound potentially dangerous factor with a compound rather dangerous feature are taken into account. The resulting mono-element fuzzy group is presented, which is also a possible event resulting from the intersection of two necessary events.

Results. It is established that the problem of predicting damage due to unfavorable circumstances corresponds to a combinatorial-type problem, which consists in enumerating all sets of arguments. The resulting range, which is an elemental group of indistinguishability, characterizes the smaller and larger possible values of the size of the group of a potentially dangerous factor with a composite rather dangerous feature. It is shown that the formulated combinatorial problems without significant changes are applicable to problems in a generalized form, when composite rather dangerous features are determined using not only the operation of intersection, but also uniting and difference; thereby, the initial groups are not necessarily the objects with simple features.

Discussion and Conclusions. The results obtained are focused on the construction of analytical algorithms for establishing indistinguishability under the monitoring, modeling, forecasting state-related processes and complex dynamic multiparameter objects.