Optimization models of repair periods of electrical equipment of self-propelled rolling stock, according to its technical condition

. Efficient use of self-propelled rolling stock (SRS) used in the installation and repair of the contact network and track circuit, only from the use of the latest technology and installations in it, but also from an increase in the reliability of each piece of SPE - (self-propelled equipment). The development and widespread introduction of technical diagnostic systems is one of the most important factors in increasing the reliability of equipment efficiency and a sharp reduction in the cost of its operation. It is known that the annual total cost of maintenance of self-propelled rolling stock continues to increase as the network of electrified railways expands. The solution to this problem is possible by increasing the operational and structural reliability and the widespread use of modern methods and technical diagnostic tools during their operation. Currently, the mechanical and electrical parts of the SRS are actually operated without diagnostic tools, therefore, without information about their actual state.


Introduction
In the practice of operation of the SPM, a system of scheduled preventive SRS maintenance is used, the frequency of which is determined by average static indicators, and not by the true indicators of each specific part of these machines.The technical and economic criteria for the SRS system is a minimum of equipment downtime on the basis of strict regulation of repair cycles.In accordance with this criterion, the frequency and scope of maintenance and repair work are determined by predetermined tonal norms to maintain reliable operation of power equipment in a strict planning environment.But the SRS system in the new economic conditions does not ensure the adoption of optimal decisions, that is, the appointment of maintenance periods is carried out regardless of the actual state of electrical equipment and installations by the time repairs begin.The use of modern diagnostic systems makes it possible to determine the actual state of each machine, taking into account its real state, therefore this article is devoted to the analysis of operating modes of operation and the development of methods for optimizing the frequency of maintenance of the SRS.The operational reliability of the SRS remains low, which leads to interruptions in the technological cycle.Therefore, the improvement of diagnostic systems, the analysis of a real assessment of the technical condition in order to increase the efficiency of their use is an urgent task [9][10][11].
SRS consists of heterogeneous devices with different technical and electrical parameters that characterize its technical condition.
The basis for optimizing the frequency of repairs of electrical equipment is the regularity of changes in reliability parameters by specific total operating costs.And complete expenditure of each resources.Electrical equipment at minimal financial and logistical costs on the other hand.In this sense, then the statement of the problem of determining the optimal frequency of equipment replacement is fair, taking into account the technical condition determined by the diagnostics of its condition.

Methods
Models for optimizing the overhaul periods of electrical equipment, taking into account the technical condition, SRS determined using technical diagnostic tools, are based on the following principles [2] • electrical equipment is subject to periodic maintenance during operation, together with which technical diagnostics are carried out; • based on the results of technical diagnostics, a decision is made on the expediency of carrying out preventive repairs; Statistical information about the occurrence of failures of electrical equipment of the SRS most fully reflects the pattern of changes in its technical condition and is characterized by the function of operational failure probability Q(T) [2]: where Рn (Т) and РB(Т) are operational probabilities of no-failure operation in case of gradual and sudden failures; T is the period of operation for which the costs and the optimal frequency of repairs are calculated.
Taking expression (1) as a function of determining the technical condition, and some integral diagnostic parameter (used resource) as an indicator of the frequency of repair work, the change in the technical condition over the time interval T at the i-th estimate ∆Qi can be represented as where Q0 is the initial value of the technical condition; Qi-1 -the value of the technical condition at the i-th assessment; Q(T) is the probability of failure of electrical equipment as a function of changes in the technical condition during the overhaul period and is corrected based on the results of technical diagnostics.
As a criterion for optimizing the frequency of repairs, the function of the minimum of the average total unit costs for the operation of electrical equipment Z(T) of the SRS was chosen.The objective function Z(T) when implementing the laying strategy for repairs of electrical equipment takes into account the change in technical condition and in most cases is determined by the following components [9][10][11].
The average unit costs for maintenance and technical diagnostics of SRS electrical equipment are: Average unit costs for post-accident repairs: where λ is the failure rate of electrical equipment.
Thus, the objective function is defined by the expression: where 3п.а.р is the cost of repairs after accidents.The need for repair of electrical equipment is taken into account the results of technical diagnostics.Let us assume that the fact that, according to the results of technical diagnostics, a repair is assigned, equals q and the fact that a repair is not assigned, equals f.In this case, q and f constitute a complete group of events, i.e., q+f=1.Then part of the costs for maintenance, diagnostics and preventive maintenance, taking into account these probabilities, will be determined by the expression The costs due to electrical equipment failures are determined from the assumption that during the time T n(T) failures can occur, caused by purely electrical and mechanical [9][10][11].
The first group of reasons is due to the factors of gradual wear of the electrical insulation of electrical equipment, which can be predicted.The number of damages from this group of causes n(T) determines the basic failure rate λb.For electrical equipment, the value of λb is determined based on the analysis of failure statistics for each unit of electrical equipment for the average value of the overhaul period.The implementation of the repair strategy, taking into account the results of technical diagnostics, involves changing the overhaul period in a wide range.Therefore, the failure rate of electrical equipment λ(t) should be determined as a function of time after each subsequent repair.Such a dependence for electrical equipment has the form [4]: The second group of reasons for failures is due to sudden factors, the change of which is not possible to predict.These include, for example, personnel errors, false protection action, natural disasters, etc.The number of failures from this group of causes nB(T) determines the variable component of the failure rate λn.
The total value of the failure rate is equal to The costs of eliminating these failures can be represented by the expression The average specific total costs, taking into account (4.7), (4.8) and (4.10), will be equal to na na Expression ( 11) is largely determined by the f-probability that, based on the results of technical diagnostics, repairs are not scheduled.If f=0, then expression (11) characterizes the costs of operating electrical equipment with a strategy of preventive maintenance (SRS).If f=1, then expression (11) characterizes the costs of operating electrical equipment performed under strategy of emergency repairs (SER), i.e. by denials.
Using model (11), one can obtain models of a number of intermediate competitive strategies (ICS).Let us introduce classification features into the model that take into account the nature of information about EO failures and the type of repair maintenance strategies that take into account or do not take into account the results of technical diagnostics.In this case, the range of f change is limited to 0<f<1, and expression (11) will characterize the strategy for operating electrical equipment according to technical condition (STC).
In practice, it is advisable to know in advance the optimal values of overhaul periods, which would take into account the actual conditions and modes of operation of electrical equipment.To do this, we differentiate equation (11) with respect to Т and solve it for dZ(T)/dT = 0.As a result, we obtain the required expression characterizing the optimal overhaul period Tопт-during the operation of electrical equipment according to the ICS and STC [10][11][12].
Substituting in (12) the value f = 0 and f = 1, we obtain, respectively, expressions for determining the optimal overhaul period Tопт during the operation of SRS electrical equipment.According to the SRS strategy (13) and the failure strategy (14) Tотк.
The obtained expressions use the critical operational failure probability QK (T), which is determined on the basis of such failure probability, the mathematical expectation of the failure rate and the unit costs of carrying out after emergency repairs.Statistical data on the operation of electrical equipment and the results of technical diagnostics [5].
For a specific type of electrical equipment, such as an electric motor, the operational failure probability is fixed and corresponds to a predetermined critical probability QK(T).In the theory of reliability, when determining the timing of preventive maintenance, the failure probability function Q(T) is described by an exponential dependence [5], since this is the simplest and most frequently used distribution law in the practice of reliability analysis and solving repair planning problems.In addition, in real operation, the volume of failure statistics is often insufficient to apply more complex laws (normal, Weibull, binomial γ distribution, etc.).At the same time, the difference between the real distribution law and the exponential one leads to insignificant errors if there is a number of static data included in a certain period in the results of determining the optimal timing of preventive measures [5].In addition, if a complex technical system with renewable elements, which includes electrical equipment, is considered at a higher hierarchical level as one element, then the law under the most general conditions can also be considered exponential [5].
To calculate the function of the operational probability of failures Q(T) at which the influence of operating modes on the need for EE in repair can be taken into account, it is proposed to use an expression of the form where t is a predetermined time interval, for example, the current month; R*j -relative change in the resource of electrical equipment in the case of its operation under j-x conditions and modes of operation [10][11][12].
When calculating Q(T) by expression (15), the value of R*j is included in the initial data as a parameter determined by the results of continuous monitoring of the operating modes of each electrical equipment of the SRS using technical diagnostic tools, for example, using the method described in.The value of λб is determined in advance and is included in the initial data in the form of constants.In this case, the values of R*j and λб, respectively, will be equal to: where K is the number of units of the same type of electrical equipment for one technological purpose; n is the average number of failures per year during the operation of K units of electrical equipment; RH is the standard value of the resource of electrical equipment; RHjФthe actual residual life of the SRS electrical equipment during its operation in j-x conditions and modes of operation.
By substituting specific data into expression (12), it is possible to obtain optimal overhaul periods, taking into account the diagnostic results.

Conclusion
The system of preventive maintenance has significant shortfalls in the transition to market conditions.The article developed a mathematical model of the objective function and obtained an expression for determining the optimal frequency of maintenance of electrical equipment of self-propelled rolling stock, taking into account heavy maintenance costs, diagnostic results and changes in reliability indicators under operating conditions.Based on the totality of all components of the maintenance parameters, a method is proposed for predicting the resource of an object's trouble-free operation.