## 1 Introduction  
The real engineering objects are not without uncertainty in determining material properties, geometric parameters, boundary conditions, applied loads, etc. In the traditional approach, the randomness of structural parameters is ensured by applying safety factors at the design stage. The most appropriate, however, is to treat the structure design process as a random event and analyze it with the methods of probability calculus. The most advanced reliability analysis methods are probabilistic methods. These methods are based on the assumption that input variables are of random character. In spatial structures, especially those exposed to vibration, it may be difficult to gain a full set of statistical information about the work of the system. Accordingly, a new very interesting trend has emerged that deals with non-probabilistic or hybrid uncertainties in reliability analysis [1]. Currently, the structural reliability theory is already a well-developed research area. The most important literature in this area includes books and monographs presenting the basics of probabilistic theory [2; 3; 4]. In early applications of reliability analysis methods, it was accepted that the limit state function is an explicit function of random variables. Such functional dependency can be realized only for very simple examples or in the case when we use artificial neural networks (NNs) to generate explicit limit state function. In practical realizations, this dependence is not explicit, and it is determined by using numerical procedures, e.g., the finite element methods. The probabilistic finite element methods for analysis of structures have become of increasing interest in recent years. These are aimed at accounting for the random nature of material properties or loads. The existing methods can be placed in two distinct categories. The first group is aimed at second-moment analysis, where the objective is computing the means and variance of response quantities. One of the methods of this type is the perturbation method, which is based on a series expansion of stiffness matrix with respect to uncertain parameters by means of Taylor expansion. The perturbation method is not, however, designed to calculate failure probability, but only to obtain moments of statistical responses of the system. Using this method to solve problems of linear elasticity theory was presented in References [5; 6; 7]. The merger of the finite element method and stochastic analysis to deal with complex problems of modern engineering was presented in the monograph. [8]. Lately, interesting works have been done by References [9; 10]. The second group is aimed at reliability analysis, where the objective is computing probabilities associated with prescribed limit states. Special attention should be paid to References [11; 12]. They present the basic concepts of reliability theory with a particular reference to their uses in civil engineering. The use of probabilistic methods in reliability analysis of steel-bar structure was shown in References [13; 14; 15; 16]. A separate group of reliability analysis methods are system reliability methods [17]. Neural networks (NNs) is the name of mathematical structures made of components (artificial neurons) and their software and hardware implementations. Neural networks, together with fuzzy systems and evolutionary algorithms, were created as a result of research conducted in the field of artificial intelligence. For many years, the development of this field was limited by the low computational capabilities of the computers. The last breakthrough came in 2006 with the development of computer technology (including graphics processing unit with a thousand cores). At that time, the so-called Deep Learning Networks with effective teaching methods were developed. However, this methodology requires access to Big Data sets or real-time data and hardware of the highest quality or access to computing servers [18; 19].