The Aim of the paper is to develop an analytical procedure for calculating the dependability indicator of a specific tree-like transporting network, i.e., the water disposal system of a major city.

Methods. It is suggested using the relative volume of sewage water released from a sewage system into the environment as the result of the failure of the former’s components as the measure of dependability. This paper presents a simple and convenient method for calculating such volume. The method is based on the representation of a tree-like sewage network as a combination of Y fragments referred to as structural elements. Every such element is formally replaced with its pseudo equivalent with a failure rate calculated assuming that the volumes of untreated waste water released by actual and fictitious elements are equal. A consistent application of this approach reduces the problem of estimation of the volume of released waste water to elementary subproblems that are solved using probability methods.

Results. The problem of identifying the operational dependability indicator comes down to a recurrent stepwise procedure for equalization of Y fragments of the network, at each step of which the calculation data from the preceding step are used as the input data. Each such step, starting from the entry network, leads to another (virtual) network, for which the procedure repeats. The equalization process ends when the original network is represented by only one pseudo element, for which the dependability indicator is defined in an elementary way.

Conclusion. The authors developed a convenient method for calculating the operational dependability indicator of a tree-like sewer network of a major city. Some practical problems are referred to that can be solved using the proposed method. Future lines of research in the domain were identified.

Aim. The signature theory allows comparing the structural dependability of complex systems consisting of identical components using a numeric vector referred to as signature that is determined using a certain algorithm. The signature describes a system’s structure and is associated with the order statistics of the components’ times to failure. The paper aims to familiarize the Russian readers with the theory, as well as to build simple algorithms that would allow finding the signature of an arbitrary VooL system, including a series parallel system using the known signatures of its subsystems.

Methods. Calculations and theorem proving primarily involve the use of combinatorics with various element selection patterns. Additionally, classical methods of the probability theory and mathematical theory of dependability are used.

Conclusions. The paper introduces such concept of the mathematical dependability theory as technical system signature. The primary purpose of this characteristic consists in comparing the structural dependability of several, in particular, two systems. The algorithm is sufficiently simple and involves comparing two finite numeric arrays according to a certain rule. Structural dependability is understood as the dependability of connection circuits of components that are identical in terms of dependability. That significantly reduces the capabilities of the signature theory, as practically all technical systems consist of components with various dependability. However, with a certain conservatism, it can be considered that all of a system’s components have a dependability identical to that of the least dependable one. The degree of conservatism will be determined by the difference in the component dependability that will be a sufficiently low value for highly dependable components. Additionally, we should note the purely mathematical beauty of the signature theory that has recently been gaining significant momentum in foreign scientific publications. It must be noted that according to the classical laws of combinatorics, as the number n of system component elements grows, the construction of a technical system signature speeds up significantly. Therefore, it becomes necessary to develop sufficiently simple algorithms for calculating the signature of a random system. As part of the presented work, analytical approaches to signature acquisition were developed for both simple cases when a single component is, in series or parallely, added to a subsystem, and more complex situations when one or more subsystems are added to another subsystem. A number of cases of signature construction were considered using both the classical method, and the one suggested in this paper. An example was analysed of system dependability comparison using their respective signatures. The structural dependability of systems with various numbers of components was compared. The paper proves a number of theorems that allow calculating the signature of a random structure diagram consisting of components that are identical in terms of dependability.

State-transition diagrams are given for the situation of monitoring that takes into consideration explicit and hidden failures.

Aim. To generate state-transition diagrams that are used in the development of the dependability model and associated calculation methods under conditions of periodic monitoring.

Methods. The method is based on the classification of failures by detection, i.e., explicit and hidden failures. Accordingly, facility condition inspection may be continuous and/or periodical. Periodical inspection is conducted at equal intervals. The state-transition diagram is generated taking into consideration the relations between the states and events, i.e., each state can be the cause of a certain event and, at the same time, a state is the consequence of an event. Similarly, each event is the cause of a state change, while at the same time being a consequence of a state. Within the time between two periodic inspections, continuous-time transitions take place due to failures. This process is described by the theory of continuous-time Markov processes. Upon the completion of a periodic inspection operation, the up state ensues if an operable item is subjected to inspection. If an item proves to be down, it is submitted to maintenance. Such transitions in discrete moments in time are described by semi-Markov processes. For a better understanding of the information set forth in the paper, a list is provided of the used terminology referring to state standards.

Results. Under the adopted failure modes within a single inspection period, state transitions are described in continuous time, while after the inspection operation they are described in discrete time. Within each inspection period, a system of differential equations is defined and solved based on the assumption of initial up state. Based on the deduced probabilities, the probabilities of a period without failures and with a failure are calculated along with the mean time of up and down states within the period with a failure. Should failures be detected, maintenance state is initiated. The probability of such transition is within the theory of semi-Markov processes. Based on the probabilities of the semi-Markov process, the mean failure-free periods are calculated. Such model adequately reflects the dependability processes of operated equipment. If the method is not fully observed, the dependability indicators may take significantly different values. Three examples of state-transition diagrams are given: taking into account only explicit failures, only hidden failures and both.

Discussion and conclusions. The presented approach with a constant (regular) inspection period allows building models that adequately reflect processes occurring in actual systems. All operations involved in the implementation of simulated processes are performed based on the theory of continuous-time Markov processes and semi-Markov processes. The operations are performed in matrix form. Such method enables mathematical operations using computers. The presented approach can be used for improving dependability models of technical systems.

Improving the efficiency of comparison of various test plans for homogeneous products is based on the use of the efficiency criterion of biased estimates C( ), where is a certain parameter estimate. The process of selecting efficient biased estimates involves the following: all parameters of the submitted estimates are to be strictly monotone; the estimates with minimal bias A( ) = b² or close to it are chosen. If, in the process of selection out of the proposed estimates, there is a single unbiased estimate, then the latter is the efficient one. For this estimate to be efficient in the class of unbiased estimates, it is required to prove the Cram r-Rao inequality for such estimate; estimates, for which inequality A = b² > D is fulfilled, i.e., the bias prevails over the value scatter of such estimate, are excluded; estimates are selected, for which the inequality D/A > 4 is fulfilled, i.e., the estimates, for which the realizations are grouped around the true quantitative value of the estimated parameter from different sides; out of the remaining estimates, the estimate with the minimum bias A( ) = b² is selected. In case a single estimate with minimum bias A has been selected, such estimate is considered efficient; in case A are equal, the estimate with minimal variance is chosen as the efficient one. As the efficiency criterion of biased estimates, characteristic C( ) = D·b² is specified. The suggested probability of no-failure (failure) estimates are to be strictly monotone in terms of all parameters and not equal to zero or one.

The Aim of the paper. The paper aims to obtain efficient estimates of the probability of no-failure for the binomial test plan and the test plan with limited time and recovery using the efficiency criterion of biased estimates.

Methods of research. A bias-efficient estimate was found using integral numerical characteristics of estimation accuracy, i.e., total squared bias of the expected realization of a certain estimate off of the examined parameters of the distribution laws, etc.

Conclusions. Bias-efficient estimates were obtained of the probability of no-failure for the binomial test plan and the test plan with limited time and recovery. The obtained probability of no-failure estimates are practically applicable as part of testing and operation of various products not associated with failures.

Aim. The paper aims to overview the opportunities, approaches and techniques of studying and ensuring functional safety of transportation systems, including those driverless, with the use of Big Data. It is noted, that the modern technology that underpins next-generation transportation systems that operate in ever-evolving conditions, with significant numbers of passengers, requires modified control systems design. With the growth of agglomerations, many suburban systems merge with urban ones, and their traffic intervals are close in size to those of the metro. Under these conditions, there is a transition from human-machine systems to automatic systems, characterized by varying degrees of automation. Widespread deployment of digital telecommunications, process automation and remote data collection and management technology is under way in railway transportation. Variations in the behaviour of transportation systems as a type of cyberphysical system cause a paradigm shift from line-andstaff to adaptive management with fundamentally non-linear systems with variable structure and parameters.

Methods. Control and management systems are conventionally assessed for Lyapunov’s stability. In this case, the behaviour of a stable system can with a 100% probability be predicted in the neighbourhood of the ε-tube. For the examined supervised systems, in which stability is ensured through the introduction of a supervisor algorithm, speaking of a strict Lyapunov’s stability would not be correct. The idea of controlled algorithms can extend not only to ANN, but also to other intelligent algorithms. Thus, a scope of systems and knowledge is identified that is not covered by the relevant regulatory documents and methods of safety case preparation. Identifying and eliminating abnormal signals of such systems would allow defining the boundaries of the set of acceptable processes more clearly, thus, in some cases, increasing the speed of the decision algorithms by disabling an entire branch of unfavourable scenarios.

Results. For non-linear transportation systems with variable stricture and parameters, examples are considered of machine learning/Big Data application in analysing the functional safety of complex control/management systems in railway transportation. The paper proposes the concept of application of supervised artificial neural networks combined with model checking. A special attention is given to artificial neural networks with control elements that are considered as a new subclass of neural networks.

Conclusion. Updated requirements are defined for transportation systems using artificial intelligence as part of adaptive train schedule management and autonomous train control. That will ultimately allow developing an entire line of research associated with the operation of complex systems with counterintuitive behaviour from AI-based system functional safety estimation and machine learning to safety case preparation of intelligent supervised control/management systems based on formal verification.

Aim. An important aspect of flight safety is associated with obtaining information on the potential performance of a pilot in emergency situations. For that purpose, the authors tested a number of currently existing deformation models of a pilot’s emotional experience in terms of the agreement between the predicted level of deformation obtained using such models and the actual level of deformation in abnormal in-flight circumstances (as the pilot’s emotional experience is what resists the destructive action of psychological stress that occurs in abnormal in-flight circumstances).

Methods. The conducted study used the following methods: interview, psychological diagnostics, mathematical simulation, expert evaluation. Professional pilots (10 people) who have a level of experience sufficient for this research were interviewed in free form on their personal involvement in abnormal situations that is later evaluated by experts in terms of deformation of emotional experience. Using a special scale, the test subjects evaluated the hazard of their respective abnormal situation, as well as estimated 18 abnormal in-flight situations out of the database collected by the Saint Petersburg State University of Civil Aviation. All study participants were also tested for neuroticism using the Eysenck Personality Inventory (EPI) (adapted by A.G. Shmeliov). Using that data and models in the form of disaster variety, the predicted deformation of the emotional experience was calculated and compared with the expert estimate.

Results. While, formally, one of the examined models (A.O. Lengarov’s model) proved to be somewhat superior as compared to the other one (S.G. Lobar’s model), but no fundamental difference between them was identified. The predictive values of emotional experience deformation loosely and insignificantly correlate (p > 0.1) with the expert estimate. For A.O. Lengarov’s model rcorr. = 0.2678, while for S.G. Lobar’s model rcorr. = 0.2199.

Conclusions. Currently, there is no proven, reliable model of emotional experience deformation. It is required to further collect, analyse and generalise data on pilot behaviour in abnormal in-flight circumstances. This study confirmed the presence of at least two out of eight “catastrophe flags” according to Rene Thom. Thus, the hypothesis that the model of a pilot’s emotional experience deformation is to have the form of fold catastrophe is correct. The method of objectification of abnormal in-flight circumstance hazard evaluation is to be significantly improved, probably, with the use of polynomial approximations, as well as by expanding the abnormal circumstance database of the Saint Petersburg State University of Civil Aviation, primarily by collecting situations involving more recent types of aircraft.

Aim. To select, out of the currently available tethered high-altitude multicopter-based platforms, the most promising one in terms of the flying characteristics. The latter are estimated based on the combination of the affecting properties of the platform.

Methods. In order to achieve the specified goal, it is suggested using the methodology for developing the model of multidimensional estimation of a platform. It uses methods of system and function analysis of a platform’s characteristics, methods and models of the theory of relations and measuring.

Results. A problem domain model and decision-maker’s preference model are suggested to be used as components of the multidimensional estimation model. The methodology is demonstrated using the case of quality estimation of five platforms.

Conclusion. The approach proposed in the paper allows using the developed methodology for estimating the quality and engineering sophistication of items of any nature. The methodology can be used for comprehensive assessment of an item in terms of dependability and survivability.

The dependability of the ABTC-MSh automatic block system entirely depends on the functional safety and operational stability of its component devices, most of which operate in pulse mode. One of the key components of pulse signal converters is various transformers and chokes, whose calculation and development is, in practice, often difficult due to insufficient consideration of stray parameters and operational specificity of such electromagnetic systems when the core is magnetized. The paper estimates the results of coordination of the transformer’s electrical characteristics with the load impedance and that of the pulse signal source suitable for analysing and constructing signal-shaping networks and delay lines based on lumped elements.

Aim. The aim of the work is to substantiate an engineering technique for calculating the duration of the leading edge of a signal in the process of setting its level at the output of the forming circuit of a pulse transformer when matching with loads and estimating the delay time for switching on the actuator at a given response threshold, depending on the parameters of the second-order circuit, which is often used as a feedback element of pulse converters and auto-regulation systems.

Methods. The time characteristics and pulse form are determined for a transformer whose equivalent circuit corresponds to the item’s operation in high frequencies and takes into account the stray parameters normalized to to the primary side. The output signal function is described in accordance with the linear electric circuit theory in operator form and, after a series of Laplace transformations, the generalized expression of the transmission factor is reduced to a standard form for a second-order circuit. The analytical solution was found by determining the values of the zeros and poles of the function on the plane of complex numbers as roots of quadratic equations expressed in terms of the coefficient of circuit damping. Graphs of the field dependences of the processes of establishing the pulse amplitude at the output of the forming circuit and the proportions of the amplitude outlier on the attenuation coefficient are given for various ratios of the coefficients of matching the transformer wave resistance with the load impedances and the pulse signal source. Point estimates of the pulse edge duration are made using the Mathcad programming function and taking into account the dimension of TRUE/FALSE matrices that reflect the transition from zero to one. This allows proposing linear approximations of the duration dependences within the given interval with a single inflection point that corresponds to the condition of complete matching of all resistances. Information is provided on the deviation of the approximation from the calculated data, the delay time of the actuator by the threshold. It is also discussed whether it is admissible to represent distributed parameters in the form of lumped elements while implementing artificial delay lines and higher-order circuits.

Results. Conclusions. The specified problem is resolved by defining a unique calculated dependence that associates the signal edge duration to the transmission coefficient of the examined second-order circuit. The validity of the method for dependence deduction is based on describing the output signal of a pulse transformer in a general form, subsequent analysis of the expression and deduction of an accurate analytical solution, taking into account the primary stray parameters of the transformer and load values.