RU2602295C1 - Method of pump station reliability evaluation - Google Patents

Abstract

FIELD: water supply.

SUBSTANCE: invention relates to water supply and water disposal systems. Method consists in that, pump station separation is performed to finite number of N elements. As i-th element of pump station, at least one pump is adopted, at least of one type in combination with all other elements of pump station, which failure leads to said pump shutdown. As pump station i-th element probability parameter sudden failures intensities λ_{i, t} are adopted, eliminated during current repairs, and their restoration of µ_{i, t} intensities, progressive failures λ_{i, k} intensities, eliminated during overhauls, and their restoration of µ_{i, k} intensities, as random value pump station delivery Q is adopted. Additionally determining finite number n of pump station conditions, j=0, 1, 2, …, n, and corresponding them pump station deliveries Q_j, as well as admissible accuracy σ_adm of random value distribution law determination and assign simulation modelling duration t. Probabilistic simulation is performed by means of pump station operation simulation modelling results data processing. If produced mean-square deviations σ₁ and σ₂ exceed admissible accuracy σ_adm of random value distribution law determination, then increasing simulation modelling duration t and repeat simulation stage until obtained mean-square deviations σ₁ and σ₂ will not decrease to admissible accuracy σ_adm, and if obtained mean-square deviations σ₁ and σ₂ does not exceed admissible accuracy σ_adm of random value distribution law determination, then by statistical analysis of pump station conditions j and corresponding them deliveries Q _j, obtained as a result of simulation modelling, obtaining of a random value Q distribution law of F(q), determining for each value q probability of, that random delivery value Q of pump station receives value is less than q, i.e. F(q) = P(Q < q).

EFFECT: method provides increase in pump station operation reliability.

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Description

The invention relates to the field of water supply and sanitation systems and can be used to determine the laws of distribution of a random flow rate of pumping stations.

A known method for assessing the reliability of pumping stations (see the article by one of the authors of this application: Ignatchik S.Yu. Energy conservation and reliability in the reconstruction of sewer pumping stations / Water supply and sanitary equipment. 2012. No. 12. P. 37-43). It allows you to determine the technological and probabilistic reliability indicators for each element of the technological part of the station, as well as the probabilistic and parametric reliability indicators of the station as a whole through a mathematical model that describes the process of changing its states in the form of a Markov random process.

This method is characterized by a narrow scope, since it is applicable only for stationary flows of failures and recoveries of equipment of pumping stations, for example, at stations equipped with pumping units for which the duration of elimination of sudden failures eliminated during ongoing repairs and gradual failures eliminated in the process of major repairs are not significantly different. However, in practice there are pumping stations for which this condition is not fulfilled, for example, stations equipped with powerful pumping units with high-voltage motors. For them, the average duration of the restoration (12000-16000 h) during the overhaul process is three orders of magnitude longer than the average duration of the restoration during the current repair (60-80 h). Such a recovery process does not meet the criteria for stationarity. For this reason, in such cases, the application of this method will lead to a decrease in the accuracy of assessing the reliability of pumping stations.

The closest analogue to the claimed method is the General logical and probabilistic method (OLVM), described in the writings of professors I. Ryabinin, G. N. Cherkesov, A. S. Mozhaev and others. For example, in the work “Comparative analysis of fault tree technologies and automated structural and logical modeling used to carry out probabilistic safety analysis of NPPs and process control systems at the design stage ”: report on R&D“ Technology-2004 ”/ FSUE SPb AEP, OJSC“ SPIK SZMA ”, IPU RAS; responsible executors: Ershov G.A., Mozhaev A.S., Viktorova B.C. St. Petersburg, - 2005, p. 21-22. In accordance with this report, the CFM includes the following four stages:

1. The stage of the structural-logical statement of the problem, which includes:

}, например, работоспособности/отказа, готовности/не готовности, поражения/не поражения и т.д. и заданными вероятностными параметрами p_i(t), или q_i(t)=1-p_i(t);- dividing the entire system under consideration into a finite number H of elements i = 1, 2, ..., H, each of which is represented in the reliability model as a simple (binary) event x _i with two possible states x _i = {x _i ,

}, for example, operability / failure, readiness / not readiness, defeat / not defeat, etc. and given probabilistic parameters p _i (t), or q _i (t) = 1-p _i (t);

выходных (интегративных) функций для каждого элемента в системе;- determination of the content and logical conditions for the implementation of y _i and / or non-implementation

output (integrative) functions for each element in the system;

- a logically rigorous verbal and graphical (analytical) description of the sets X of individual elements of the system and the set of conditions Y of their implementation of their system functions, which together G (X, Y) form a special functional integrity scheme (SFC) of the system in question;

реализации основных функций и/или возникновения опасных состояний системы;- a logically strict description and assignment using separate or group output (integrative) functions of the logical functioning criteria (LCF) of the system

implementation of the basic functions and / or occurrence of dangerous conditions of the system;

Логическая ФРС позволяет аналитически строго, но в компактной форме, определить все комбинации состояний элементов

, в которых (и только в которых) система реализует свою выходную функцию F.2. The stage of logical modeling, at which, using special conversion methods of the SFC and LFF, the logical function of the system’s health (FRS) is built

Logical Fed allows analytically strict, but in a compact form, to determine all combinations of element states

in which (and only in which) the system realizes its output function F.

3. The stage of probabilistic modeling, in which, using special methods of the Fed conversion, the polynomial of the calculated probabilistic function (WF) P _F ({p _i (t), q _i (t)}, i = 1, 2, ..., H; t). The WF polynomial allows one to strictly analytically determine the law of the distribution of the system uptime for the implementation of the output function F, given by the logical criterion of operation.

4. The stage of calculating the reliability indicators, which are performed on the basis of the WF and the specified parameters of the reliability of the elements.

This method is characterized by limited functionality, because:

- with its help, it is impossible to determine technological reliability indicators in the form of distribution not of uptime, but of a technological parameter, for example, the supply of a pumping station, taking into account the hydraulic laws of the pumps working together;

- with its help it is impossible to evaluate the reliability of a system consisting of elements whose process of changing states (operational and failure) occurs under the influence of two random flows (exit to current and overhaul repairs, the durations of which differ by an order of magnitude or more), because there is no logical connection between these events.

The objective of the present invention is to expand the functionality of the known method.

The problem is solved in that in the known method containing the stages in which:

a) carry out the separation of the entire system in question into a finite number H of elements i = 1, 2, ..., H, each of which is represented in the reliability model as a simple (binary) event with two possible states, for example, operability / failure and probability parameters;

b) carry out probabilistic modeling with the definition of the law of distribution of a random variable, in accordance with the present invention:

1. At least one pump of at least one type in combination with all other elements of the pump station, the failure of which leads to a halt in the operation of said pump, is taken as the ith element of the pump station.

2. As the probabilistic parameters of the ith element of the pumping station, take the intensities of sudden failures λ _{i, t} eliminated during the current repairs, and the intensities of their recoveries µ _{i, t} , the intensities of the gradual failures λ _{i, k} eliminated during the overhauls, and the intensities of their recoveries µ _{i, k} .

3. As a random variable, the flow Q of the pumping station is taken.

In addition, at step a), a final number n of states of the pumping station, j = 0, 1, 2, n, and the corresponding feeds Q _{j of the} pumping station, as well as the permissible accuracy σ are _additionally determined for _additionally determining the distribution law of a random variable and the duration t simulation modeling.

At the same time, probabilistic modeling at stage b) is carried out by processing the data of the simulation results of the operation of the pumping station, during which:

in parallel, generate a series of random processes from two flows of random operating time and recoveries of elements of the pumping station, one of which with the intensity of sudden failures λ _{i, t} and the recovery rate µ _{i, t} , the second with the intensity of gradual failures λ _i , _k and the recovery rate µ _{i, k} ;

determine the standard deviations for the elements of the pumping station of each type

where m ₁ , m ₂ is the total number of random processes in a series of t random times between sudden failures that are eliminated in the process of current repairs, and gradual failures that are eliminated in the process of overhauls, t _{1, ii} , t _{2, ii} are the average values for random running processes between sudden failures eliminated in the process of current repairs and gradual failures eliminated in the process of major repairs,

and, if the obtained standard deviations σ ₁ and σ ₂ exceed the permissible accuracy σ _additional determination of the distribution law of a random variable, then increase the duration t of simulation and repeat step b) until the obtained standard deviations σ ₁ and σ ₂ are reduced to an acceptable accuracy σ _add

and, if the obtained standard deviations σ ₁ and σ ₂ do not exceed the permissible accuracy σ _additional determination of the distribution law of a random variable, then by statistical analysis of the states j of the pumping station and the corresponding flows Q _j obtained as a result of simulation, we obtain the distribution law F (q ) a random variable Q, which determines, for each q value, the probability that the random supply quantity Q of the pumping station takes a value less than q, i.e. F (q) = P (Q <q).

Distinctive features of the proposed method are:

1. The adoption as the i-th element of the pumping station, at least one pump, at least one type in conjunction with all other elements of the pumping station, the failure of which leads to a halt of the said pump;

2. The acceptance as the probability parameters of the i-th element of the pumping station of the intensities of sudden failures λ _{i, t} eliminated in the process of current repairs, and the intensities of their recoveries µ _{i, t} , the intensities of gradual failures λ _{i, k} eliminated in the process of overhauls, and the intensities of their recoveries µ _{i, k} ;

3. Acceptance of a pumping station Q as a random variable;

4. An additional determination at step a) of a finite number n of states of the pumping station, j = 0, 1, 2, ..., n, and the corresponding feeds Q _{j of the} pumping station;

5. Additional determination in step a) _additional admissible σ accuracy of determining the law of distribution of the random variable;

6. Additional appointment at stage a) the duration t of simulation;

7. The implementation at stage b) of probabilistic modeling by processing data of the results of simulation modeling of the pump station;

8. Parallel generation during the simulation of the operation of the pumping station for the duration t of a series of random processes from two flows of random operating time and restoration of the pumping station elements, one of which with the intensity of sudden failures λ _{i, t} and the recovery rate µ. _{i, t} , the second - with the rate of gradual failures λ _{i, k} and the recovery rate µ _{i, k} ;

9. Determination of standard deviation for the elements of the pumping station of each type

where m ₁ , m ₂ is the total number of random processes in a series of t random times between sudden failures that are eliminated in the process of current repairs, and gradual failures that are eliminated in the process of overhauls, t _{1, ii} , t _{2, ii} are the average values for random running processes between sudden failures eliminated in the process of current repairs and gradual failures eliminated in the process of major repairs;

10. An increase in the duration t and the repetition of step b) until the obtained standard deviations σ ₁ and σ ₂ decrease to an acceptable accuracy σ _add ;

11. Determination of the distribution law of a random variable by statistical analysis of the states j of the pumping station and the corresponding flows Q _j obtained as a result of simulation;

12. Obtaining the distribution law F (q) of the random variable Q, which determines for each q value the probability that the random supply quantity Q of the pumping station will take a value less than q, i.e. F (q) = P (Q <q).

According to the information available to the authors, all the distinguishing features are not known. Their combined use allows you to expand the functionality of the method, because:

- with his help, it becomes possible to determine technological reliability indicators in the form of a random variable distribution - a technological parameter, for example, a pumping station supply. This was made possible thanks to the combined use of distinctive features No. 1 - 4, 11, 12;

- with its help, it becomes possible to evaluate the reliability of a system consisting of elements, the process of changing states (operational and failure) of which occurs under the influence of two random flows (current and overhaul repairs, the duration of which differ by an order of magnitude), between which there is no logical connection . This was made possible thanks to the combined use of distinctive features No. 1, 2, 5-11.

A brief description of the drawings.

In FIG. 1 is a plan view of a pumping station; FIG. 2 shows a section through a pumping station along one of the pumps, from which the composition of the ith element of the pumping station is visible, FIG. 3 is a table with the calculation results of the feeds Q _{j of the} pumping station in all states j = 0, 1, 2, ..., n, in FIG. 4 is a diagram with an example of the results of generating two flows from a series of random operating time and recoveries of elements of a pumping station, FIG. 5 is a graph with the pattern of variation of the standard deviation σ ₁ between the average operating time of the pumps between failures taken as initial data and obtained as a result of the simulation, depending on the duration t of the simulation, in FIG. 6 shows the results (in graphical form) of determining the desired dependence of the distribution of a random variable; FIG. 7 is a function of the distribution density f (q) of a random supply quantity Q of the pumping station, obtained by differentiating the distribution of the random variable.

The implementation of the invention.

At stage a), the entire system under consideration is divided into a finite number H of elements i = 1, 2, ..., H, each of which in the reliability model is represented as a simple (binary) event with two possible states, for example, operability / failure and probabilistic parameters.

To illustrate the features of this step in FIG. 1 is a plan view of a pumping station including a housing 1, a receiving tank 2, and equipped with two types of pumps: high-performance pumps 3 (7 pcs., Pump model - ФВ 22700/63, estimated flow - 17.0 thousand m ³ / h) and low-performance pumps 4 (4 pcs., pump model - ФВ 9000/63, rated flow - 7.5 thousand m ³ / h). Pumps 3 and 4 are located in engine room 5. In addition to FIG. 2 shows a section of a pumping station according to one of the pumps, from which the composition of the i-th element of the pumping station is visible, including, for example:

one pump 6;

elements of an automated control system (ACS) 7;

electric motor 8;

a system 9 for supplying water for cooling an electric motor; hydraulic jacks 10;

shaft 11;

system 12 for supplying water to the shaft and bearing seals;

suction pipe 13;

pressure pipe 14;

a valve 15 mounted on the suction pipe 13;

the valve 16 mounted on the pressure pipe 14.

Thus, the final number of elements of the pumping station is H = 11, each of which can be in only two states: operability and failure. In each of these elements, in the event of failure of one of its aforementioned structural parts, indicated by positions 6-16, the entire element will be in a state of failure. For example, if the valve 15 installed on the suction pipe 13 fails, water will stop flowing into the pump 6 and the whole element will not work. In the state of operability, the i-th element will be only when all its parts are operational.

The probabilistic parameters of the ith element of the pumping station are the intensities of sudden failures λ _{i, t} eliminated during the current repairs, and the intensities of their recoveries µ _{i, t} , the intensities of the gradual failures λ _{i, k} eliminated during the overhauls, and the intensity their recoveries µ _{i, k} . The indicated probabilistic parameters can be obtained in the process of technical inspection of the pumping station or from the reference literature. For example, the survey found that:

- the first type of the i-th element, which includes high-performance pumps ФВ 22700/63, has the following probabilistic parameters - the intensity of sudden failures λ _{i, t} = 32.6082 * 10 ^-4 , 1 / h, the intensity of their recoveries µ _{i, t} = 125.00 * 10 ^-4 , 1 / h, the rate of gradual failures λ _{i, k =} 0.83333 * 10 ^-4 , 1 / h, eliminated during the overhaul, and the intensity of their restoration µ _{i, k} = 0 9375 * 10 ^-4 , 1 / h;

- the second type of the i-th element, which includes low-performance pumps ФВ 9000/63, has the following probabilistic parameters - the intensity of sudden failures λ _{i, t} = 29.2213 * 10 ^-4 , 1 / h, the intensity of their recoveries µ _{i, t} = 222.22 * 10 ^-4 , 1 / h, the rate of gradual failures λ _{i, k} = 0.83333 * 10 ^-4 , 1 / h, eliminated during the overhaul, and the intensity of their restoration µ _{i, k} = 0 , 9375 * 10 ^-4 , 1 / h.

As a random variable, the flow Q of the pumping station is taken.

In step a), additionally:

- determine the final number n of states of the pumping station, j = 0, 1, 2, ..., n, and the corresponding feeds Q _{j of the} pumping station. The final number n of states depends on the finite number H of elements, as well as the number of their types. If the pumping station consists of H of the same type of elements, then the number of states is n = H + 1. At the same time, in state 0, all elements are operational. In this example, the number of states of elements with four low-performance pumps is 5, and with seven high-performance pumps it is 8. Then the total number of states of the pumping station is n = 5 * 8 = 40, i.e. j = 0, 1, 2, ..., 39. The flow rate in each state is determined by the sum of the flows of all pumps in operable state. For example, in state 0, when all the pumps are operational, Q ₀ = 7 * 17.0 + 4 * 7.5 = 149 thousand m ³ / h. The results of the calculation of feeds in all other states are shown in the table in FIG. 3. In it, k _VP , k _NP - the number of failed high-performance and low-performance pumps;

- additionally assign the permissible accuracy σ _additional definition of the law of distribution of a random variable. In accordance with the present invention, depending on the importance of the pumping station in the drainage system, any accuracy σ _add. As a rule, it is taken equal to the accepted accuracy of engineering calculations, i.e. 5%;

- designate the duration t of simulation.

Probabilistic modeling in step b) is carried out by processing the data of the simulation results of the operation of the pumping station for a duration t. Simulation is known in the art and is readily understood by those skilled in the art. For example, its definition is contained in Wikipedia (https://ru.wikipedia.org): “Simulation (situational modeling) is a method that allows you to build models that describe processes as they would in reality. Such a model can be “lost” in time both for one test and for a given set of them. The results will be determined by the random nature of the processes. Based on these data, you can get fairly stable statistics. "

In the process of simulation:

1. At the same time, a series of random processes is generated from two flows of random operating time and recoveries of elements of the pumping station, one of which with the intensity of sudden failures λ _{i, t} and the recovery rate µ _{i, t} , the second with the intensity of gradual failures λ _{i, k} and the intensity recoveries µ _{i, k} . The generation of random streams is known in the art and is readily understood by those skilled in the art. For example, its definition is contained in Wikipedia (https://ru.wikipedia.org) in the section "Generating random numbers". Generation is carried out using "various pseudo-random number generators, for each of which a specific distribution can be set." Currently, a pseudo-random number generator is available on any computer and is used as a function in most calculation programs, for example, in Microsoft Excel. To illustrate in FIG. Figure 4 shows an example of such a generation of a single stream of random operating time and recovery of elements of a pumping station of the same type, which includes low-performance pumps. As a result, received:

- the flow of random operating time t _1,1 , t _1,2 , t _1,3 , t _1,4 , ... between sudden failures eliminated in the process of current repairs (position 17 in Fig. 4). They are obtained taking into account the fact that the probability P (dt) of the transition from the operational state to the failure state during the time interval dt is P (dt) = λ _{i, t} dt = 29.2213 * 10 ^-4 * dt. When dt = 1 h, P (dt) = 29.2213 * 10 ^-4 . The result is, for example, the following stream of developments: 350.25; 334.60; 338.39; 365.44 etc. hours;

- stream of random recoveries τ_1,1, τ_1,2, τ_1.3, τ_1.4, ... during ongoing repairs (item 18 in FIG. 4). They are obtained taking into account the fact that the probability P (dt) of the transition from the failure state to the operability state during the time interval dt is P (dt) = μ_{i, t} dt = 222.22 * 10^-four* dt. When dt = 1 h, P (dt) = 222.22 * 10^-four. As a result, for example, the following recovery stream was obtained: 76; 81; 79; 81 etc. hours;

- the flow of random operating time t _2,1 , t _2,2 , t _2,3 , t _2,4 , ... between the gradual failures eliminated in the process of major repairs (position 19 in Fig. 4). They are obtained taking into account the fact that the probability P (dt) of the transition from the operational state to the failure state during the time interval dt is P (dt) = λ _{i, k} dt = 0.83333 * 10 ^-4 * dt. At dt = 1 h, P (dt) = 0.83333 * 10 ^-4 . The result is, for example, the following stream of developments: 12050; 12100; 11780; 12001 etc. hours;

- stream of random recoveries τ _2,1 , τ _2,2 , τ _2,3 , τ _2,4 , ... in the process of major repairs (item 20 in Fig. 4). They are obtained taking into account the fact that the probability P (dt) of the transition from the failure state to the operability state during the time interval dt is P (dt) = µ _{i, k} dt = 0.9375 * 10 ^-4 * dt. At dt = 1 h, P (dt) = 0.9375 * 10 ^-4 . As a result, for example, the following recovery stream was obtained: 10424.54; 6,888.35; 10,682.65; 8052.34 etc. hours.

2. Determine the standard deviations for the elements of each type.

and, if the obtained standard deviations σ ₁ and σ ₂ exceed the permissible accuracy σ _additionally determining the distribution law of a random variable, then increase the duration t and repeat step b) until the obtained standard deviations σ ₁ and σ ₂ decrease to an acceptable accuracy σ _add .

Features of this step are shown in FIG. 5, where, using the example of restoring elements of a pumping station of the same type, which includes high-performance pumps, it is shown how σ ₁ (in%) changes depending on the duration t of simulation. In this figure, position 21 denotes the average operating time of the pumps between failures in the same series, obtained by the same simulation method, position 22 denotes the average time between failures, taken as the initial data and equal to 1 / λ _{i, t} = 1 / 32.6082 * 10 ⁴ = 306 hours, position 23 is the sought standard deviation σ ₁ between the average operating time of the pumps between failures accepted as initial data and obtained as a result of the simulation.

From FIG. 5 it is also seen that if the admissible accuracy σ of the _additional determination of the distribution law of a random variable is taken to be 5%, then it will be necessary to repeat step b) until the duration t reaches 100 years.

Further, by statistical analysis of the pumping station states j and their corresponding flows Q _j obtained as a result of simulation, we obtain the distribution law of a random variable F (q), which determines for each q value the probability that the random flow quantity Q of the pump station takes a value less q, i.e. F (q) = P (Q <q).

In FIG. Figure 6 shows in graphical form the results of determining the desired distribution law of the random variable F (q) obtained by statistical analysis of the states j of the pumping station and the corresponding flows Q _j .

In addition, in FIG. 7 shows the density distribution function f (q) of the pump station q flows. It is obtained by differentiating the function F (q), i.e. f (q) = F ′ (q). The calculated distribution density function f (q) in FIG. 7 is indicated by 24. In addition, position 25 denotes the actual distribution density function f (q) of the supply q (taken as an example) of the pumping station obtained by statistical processing of operational information stored in the databases of the automated control system for a period of 5 years.

A comparison of the obtained density distribution functions (calculated, indicated by 24, and actual, indicated by 25), proves the high accuracy of predicting the flow of the pumping station in this way. Since the example is implemented using a conventional personal computer, this proves its industrial applicability.

Claims (1)

A method for assessing the reliability of a pumping station, comprising the steps of:
a) carry out the separation of the entire system in question into a finite number H of elements i = 1, 2, ..., H , each of which is represented in the reliability model as a simple event with two possible states, for example, operability / failure and probabilistic parameters;
b) is performed with a probabilistic modeling definition of random variable distribution law, characterized in that the i th at the pump station receiving element least one pump, at least one type together with all other components of the pumping station, where failure It leads to stopping operation of said pump, as probabilistic parameters i -th element of the pumping station receiving intensity sudden failures λ _{i, t,} are fixed in the current repair, and the intensity of the restored eny μ _{i, t,} intensity gradual failures λ _{i, k,} are fixed during overhauls, and the intensity of their rebounds μ _{i, k,} as a random variable taking feed pump station Q,
at step a), an additional final number n of states of the pumping station, j = 0, 1, 2, ..., n , and the corresponding feeds Q _{j of the} pumping station, is determined, as well as the permissible accuracy σ of the _additional determination of the distribution law of the random variable and the duration t simulation modeling;
probabilistic modeling at stage b) is carried out by processing the data of the simulation results of the operation of the pumping station, during which: a series of random processes are generated in parallel from two flows of random operating time and restoration of the pumping station elements, one of which with the rate of sudden failures λ _{i, t}
and the recovery rate µ _{i, t} , the second - with the rate of gradual failure λ _{i, k} and the recovery rate µ _{i, k} , determine the standard deviations for the elements of the pumping station of each type

,

,
where m ₁ , m ₂ is the total number of random processes in a series of t random times between sudden failures that are eliminated in the process of current repairs, and gradual failures that are eliminated in the process of overhauls, t _{1, ii} , t _{2, ii} are the average values for random running processes between sudden failures eliminated in the process of current repairs and gradual failures eliminated in the process of overhauls, and if the obtained standard deviations σ ₁ and σ ₂ exceed the permissible accuracy σ _additional of the distribution law of a random variable, then increase the duration t of simulation and repeat step b) until the resulting standard deviations σ ₁ and σ ₂ are reduced to an acceptable accuracy σ _add , and if the obtained standard deviations σ ₁ and σ ₂ do not exceed admissible σ _additional accuracy determination random variable distribution law, by statistical analysis of states j of the pumping station and the corresponding feed Q _j, obtained by simulation modelirova Ia, prepared law F (q) the distribution of the random variable Q, which determines for each value of q probability that a random variable flow Q of pumping station will assume a value smaller than q, that is,

.

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