CN117875947A - Reliability evaluation and maintenance decision method and system for k/n load balancing system - Google Patents
Reliability evaluation and maintenance decision method and system for k/n load balancing system Download PDFInfo
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Abstract
The application disclosesk/nA reliability assessment and maintenance decision method and system of a load balancing system relate to the technical field of equipment maintenance, and a first system state transition diagram and a first state transition intensity matrix are obtained by means of Markov process calculation according to failure rate and system state when all life cycle states of a component are transferred; calculating a first probability that the system is in different system states at any moment; to be included in the first system state transition diagramCombining some failure states into an absorption state, calculating to obtain a second probability function in the absorption state, calculating to obtain a reliability function according to the second probability function, and obtaining the critical service life of the system according to a reliability threshold; and calculating the expected total operation and maintenance cost and the expected total operation and maintenance time of the system in the critical service life, and calculating the expected operation and maintenance cost in the unit time of the system to obtain the optimal detection time interval of the system. The method and the device can reduce the operation and maintenance cost of the load balancing system.
Description
Technical Field
The application relates to the technical field of equipment maintenance, in particular to a device for repairing a piece of equipmentk/nReliability assessment and maintenance decision method and system for load leveling system.
Background
Reliability, safety, and economy of multi-component systems typically depend on the use of redundancy techniques.k/nLoad leveling systems are a typical example of redundancy techniques, requiring at least k components to operate properly. Such system configurations are widely used in a variety of industrial systems, such as multi-engine aircraft, multi-generator power plants, multi-pump hydraulic power conversion stations, and multi-computer local area networks. As components in these systems bear higher load levels, their failure rates increase, making the system more prone to failure with significant losses. Thus, rational reliability assessment and preventive maintenance strategies are aimed at improvingk/nThe operation safety of the load balancing system is important.
Periodic inspection and state-based maintenance are among the most common but also important solutions, which can effectively improve system safety and reduce operational losses. At present, an optimal maintenance strategy based on inspection is usually established by taking inspection intervals as optimization variables and costs as optimization targets. However, most maintenance decisions are to consider the stable and failure states of the components, neglecting the wear state, which leads to expensive maintenance costs. In addition, fork/nThe load leveling system, the independence assumption of the components also does not apply. When a component in the system fails, the load born by the component is redistributed to the component which works normally, so that the failure rate of the component which works normally is increased. The failure rate of the components is affected by the load level and has random dependence.
Disclosure of Invention
The purpose of the present application is to provide a method ofk/nThe reliability evaluation and maintenance decision method of the load balancing system can consider the influence of the three-state characteristics of the components and the random dependence caused by the load balancing on the state transition process of the system, and reduces the operation and maintenance cost of the system.
Based on the above object, the present application provides a method ofk/nThe reliability assessment and maintenance decision method of the load balancing system, the system is made up of n identical components, wherein, k components work normally to guarantee the system to work normally, the method includes the step:
s1, defining the total life cycle states of components to comprise a stable state, a wear state and a failure state, determining the system state based on the total life cycle states of all components in a system, constructing a first system state transition diagram according to failure rate and the system state when all the life cycle states of the components are transitioned, and calculating to obtain a first state transition intensity matrix, wherein the system state is used for representing the number of the components in the wear state and the failure state in the system;
s2, calculating first probabilities of different system states of the system at any moment according to a first state transition intensity matrix and by using a Chapman-Kolmogorov equation;
s3, combining all the states of the system in the first system state transition diagram in failure into an absorption state, constructing a second state transition intensity matrix by using a Markov process, calculating a second probability function of the system in the absorption state by using a Chapman-Kolmogorov equation, calculating a reliability function according to the second probability function, and obtaining the critical service life of the system according to a preset reliability threshold;
s4, calculating the expected total operation and maintenance cost and the expected total operation and maintenance time of the system in the critical service life according to the first probability, and calculating the expected operation and maintenance cost in the unit time of the system to obtain the optimal detection time interval of the system.
Further, step S1 includes:
the system state is set to be denoted as a ij Wherein i is represented as the number of components of the system in a failure state, and j is represented as being inTotal number of parts in failure and wear state;
setting the failure rate of the component from the steady state to the wear state as a first failure rate lambda 21 The failure rate of the component from the worn state to the failure state is the second failure rate lambda 10 The failure rate of the component from the steady state to the failure state is a third failure rate lambda 20 ；
When i parts fail in the system, the failure rate of the non-failed parts in the system from the stable state to the wear state is the fourth failure rate, the failure rate of the non-failed parts in the system from the wear state to the failure state is the fifth failure rate, the failure rate of the non-failed parts in the system from the stable state to the failure state is the sixth failure rate, the fourth failure rateFifth failure rate->Sixth failure rate->Expressed as:
；
where n represents the total number of components in the system, γ represents a non-negative constant load factor, i represents the number of components in the system that are in a failure state, i=0, 1,2 …, n-k;
and calculating the transition intensity among all the system states in the first system state transition diagram according to the first system state transition diagram, the fourth failure rate, the fifth failure rate, the sixth failure rate and the number of parts in a stable state and a wear state in the system so as to obtain a first state transition intensity matrix.
Further, step S2 includes:
is provided withSystem state a at time t ij Is the first of (1)The probability function is constructed according to the first state transition intensity matrix to obtain a Chapman-Kolmogorov differential equation, wherein the Chapman-Kolmogorov differential equation is as follows:
；
wherein,expressed in timetThe system is in system state a (i-1)(j-1) Probability of->Expressed in timetThe system is in system state a i(j-1) Probability of->Expressed in timetThe system is in system state a (i-1)j Probability of->1 of the (n-j) steady state components are represented as having undergone a state transition,/->1 of the components representing (j-i) the wear state is subjected to a state transition,/->Representing that 1 of the (n-j+1) steady state components have undergone a state transition,/v>1 of the components representing the (j-i+1) wear states undergoes a state transition;
and solving the differential equation by adopting a numerical method, and calculating to obtain the first probability that the system is in different system states at any moment.
Further, step S3 includes:
combining all the states of the systems in the first system state transition diagram into an absorption state, reconstructing the first system state transition diagram by using a Markov process to obtain a second system state transition diagram, accumulating the transition intensity from any one of the non-invalid system states in the second system state transition diagram to each invalid system state, and taking the accumulated sum as the transition intensity from the non-invalid system state to the absorption state to obtain the transition intensity from each non-invalid system state to the absorption state, and obtaining a second state transition intensity matrix;
calculating a second probability function P of the system in an absorption state by using a Chapman-Kolmogorov equation F (t) according to a second probability function P F And (t) calculating a reliability function R (t) as follows:
。
further, step S4 includes:
will critical life T c Divided into N detection time intervals T IN According to the first probability that the system is in different system states at any moment, the probability that the system needs to execute detection at the mth detection time interval is as follows:
；
wherein t is m-1 =(m-1)T IN ，t m =mT IN M represents an mth detection time interval,representing t m-1 Probability of being in state at the moment;
according to the probability of the system executing detection, the expected detection times of the system in the critical life are calculated as follows:
；
in the process of system state transition, from the first system state a 00 Initially in system state a ij Is calculated from the matrix N, wherein,
；
wherein I is an identity matrix, Q is a transient portion of a second state transition intensity matrix, and a first row of matrix N represents a state a of the system 00 Before starting to enter the absorption state, in the system state a ij Is a desired number of times;
the system is in system state a ij Is set to be a desired time E (T) ij ) The method comprises the following steps:
；
wherein N is ij Represented as system state slave a 00 Transfer to a ij Is a desired number of times;
the expected total run time E (T) of the system is:
。
further, step S4 includes:
when the system is in state a ij Running cost per unit time at (i.ltoreq.n-k)The method comprises the following steps:
；
wherein c 2 Representing the running cost per unit time when the component is in steady state,c 1 representing the running cost per unit time when the component is in a worn state;
total cost of operation C OP The sum of the expected time for each system state within each inspection interval multiplied by the running cost per unit time for that system state is expressed as:
。
further, step S4 includes:
when the system is in state a ij Preventive maintenance costs when (i.ltoreq.n-k)The method comprises the following steps:
；
wherein c PM Denoted as fixed cost of performing one preventive maintenance activity c r1 Expressed as the replacement costs of the individual parts in wear and tear conditions c r0 Denoted as replacement cost of a component in a failure state;
total cost of preventive maintenance C PM Expressed as:
。
further, step S4 includes:
when the system is in state a ij Corrective maintenance costs at (i=n-k+1)The method comprises the following steps:
；
corrective maintenance total cost C CM The method comprises the following steps:
；
calculating the total cost of detection C based on the expected detection times E (IN) of the system IN the critical lifetime N Expressed as:
C N =E(IN)* C IN ；
wherein C is IN Representing the cost of each test;
the expected total operating cost of the system over the critical lifetime, E (C), is:
E(C)= C OP +C PM +C CM + C N 。
further, step S4 includes:
according to the expected total operation and maintenance cost E (C) and the expected total operation and maintenance time E (T) of the system, calculating to obtain the expected operation and maintenance cost CPT in the unit time of the system as follows:
；
carrying out optimization model processing on expected operation and maintenance cost CPT in unit time, wherein the optimization model is expressed as:
；
and carrying out optimization algorithm processing on the optimization model to obtain a detection time interval which enables CPT to be minimum, wherein the detection time interval is the optimal detection time interval of the system.
Based on the above object, the present application provides a method ofk/nA reliability evaluation and maintenance decision system of the load balancing system,k/nthe load balancing system consists of n identical components, the normal operation of k components ensures the normal operation of the system, and the reliability evaluation and maintenance decision system comprises:
the system state transition diagram module is used for defining the full life cycle states of the components, including a stable state, a wear state and a failure state, determining the system state based on the full life cycle states of all the components in the system, constructing a first system state transition diagram according to failure rate and the system state when the full life cycle states of the components are transitioned, and calculating to obtain a first state transition intensity matrix, wherein the system state is used for representing the number of the components in the wear state and the failure state in the system;
the probability calculation module is used for calculating the first probability of the system in different system states at any moment according to the first state transition intensity matrix and by using a Chapman-Kolmogorov equation;
the reliability calculation module is used for combining all the states of the systems in the first system state transition diagram in failure into an absorption state, constructing a second state transition intensity matrix by using a Markov process, calculating a second probability function of the systems in the absorption state by using a Chapman-Kolmogorov equation, calculating a reliability function according to the second probability function, and obtaining the critical service life of the system according to a preset reliability threshold;
and the optimal model calculation module is used for calculating the expected total operation and maintenance cost and the expected total operation and maintenance time of the system in the critical service life according to the first probability, and calculating the expected operation and maintenance cost in the unit time of the system so as to obtain the optimal detection time interval of the system.
The method and the device can solve the technical problem of untimely component maintenance caused by the traditional two-state component system maintenance strategy, reduce the system maintenance cost and better guide the system maintenance strategy aiming at the three-state characteristics of the stable state, the abrasion state and the failure state of the component and the influence of random dependence caused by load balancing on the system state transfer process.
Drawings
FIG. 1 is a block diagram provided according to an embodiment of the present applicationk/nA flow chart of a reliability evaluation and maintenance decision method of the load balancing system;
FIG. 2 is a schematic diagram of a first system state transition diagram provided in accordance with an embodiment of the present application;
FIG. 3 is a schematic diagram of failure rates in transitioning between full life cycle states of a component provided in accordance with an embodiment of the present application;
FIG. 4 is a schematic diagram of the state transition strengths associated with a state of a system provided according to an embodiment of the present application in different states;
FIG. 5 is a block diagram provided according to an embodiment of the present applicationk/nA system block diagram of a reliability assessment and maintenance decision system of the load leveling system;
fig. 6 is a schematic structural diagram of a computer device according to an embodiment of the present application.
Detailed Description
The present application will be described in detail with reference to the specific embodiments shown in the drawings, but these embodiments are not limited to the present application, and structural, method, or functional changes made by those skilled in the art according to these embodiments are included in the protection scope of the present application.
Referring to fig. 1, an embodiment of the present application provides a method fork/nReliability assessment and maintenance decision method for load leveling system, the method comprisingk/nThe load balancing system consists of n identical components, wherein k components work normally to ensure that the system works normally, and the method comprises the following steps:
s1, defining the total life cycle states of components to comprise a stable state, a wear state and a failure state, determining the system state based on the total life cycle states of all components in a system, constructing a first system state transition diagram according to failure rate and the system state when all the life cycle states of the components are transitioned, and calculating to obtain a first state transition intensity matrix, wherein the system state is used for representing the number of the components in the wear state and the failure state in the system;
s2, calculating first probabilities of different system states of the system at any moment according to a first state transition intensity matrix and by using a Chapman-Kolmogorov equation;
s3, combining all the states of the system in the first system state transition diagram in failure into an absorption state, constructing a second state transition intensity matrix by using a Markov process, calculating a second probability function of the system in the absorption state by using a Chapman-Kolmogorov equation, calculating a reliability function according to the second probability function, and obtaining the critical service life of the system according to a preset reliability threshold;
s4, calculating the expected total operation and maintenance cost and the expected total operation and maintenance time of the system in the critical service life according to the first probability, and calculating the expected operation and maintenance cost in the unit time of the system to obtain the optimal detection time interval of the system.
The present invention is directed tok/nThe load balancing system considers the full life cycle states of the components, and constructs a system state transition diagram by using a Markov process according to the failure rate of each full life cycle state of the components, so as to determine that the system is not in any momentAnd (3) under the critical service life of taking the reliability as the constraint, constructing an operation and maintenance cost model in unit time, and determining the optimal detection time interval of the system, so that the maintenance and operation cost of the system is lower. The system has the following characteristics: the system consists of n identical components, wherein the normal operation of the system can be ensured by the normal operation of k components; the system is highly integrated, and when a certain component needs to be replaced, all components must be replaced at the same time; the system load is evenly distributed across all the components that are working properly.
The present application defines the full life cycle state of a component, taking into account the wear state of the component, and thus defines the full life cycle state of the component to include steady state, wear state, and failure state. It will be appreciated that a steady state refers to a state where the failure rate of the component is low, a worn state refers to a state where the failure rate of the component is high, and a failed state refers to a state where the component is completely failed. The components in both the steady state and the worn state are operational and the components in the disabled state are disabled. Based onk/nThe full life cycle status of each component in the load leveling system determines the system status, which can be expressed as a ij Where i is the number of components in which the system is in a failure state and j is the total number of components in a failure state and in a wear state. According to the system state a ij The state transition process of the system is modeled by using a markov process to obtain a first system state transition diagram, as shown in fig. 2. In the one-step state transition process in the first system state transition diagram, there are three possible system state transitions: from state a aj Transition to state a i(j+1) Indicating a transition of a component from a steady state to a worn state; from state a ij Transition to state a (i+1) j Indicating a transition of a component from a worn state to a disabled state; from state a ij Transition to state a (i+1) (j+1) Indicating that there is a direct transition of a component from a steady state to a disabled state. When i=n-k+1, the system state is the failure state.
Setting the failure rate of the component from the steady state to the wear state as a first failure rate lambda 21 From abrasion of partsThe failure rate of the state transition to the failure state is the second failure rate lambda 10 The failure rate of the component from the steady state to the failure state is a third failure rate lambda 20 . The first failure rate, the second failure rate, and the third failure rate are all related to the load level of the system, and when there is a component failure in the system, the load borne by the component will increase to other components that are not failed, resulting in an increase in the failure rate of the components that are not failed, as shown in the failure rate diagram at the transition between the full life cycle states of the components shown in fig. 3. Therefore, when i parts fail in the system, the failure rate of the non-failed parts in the system from the steady state to the worn state is the fourth failure rate, the failure rate of the non-failed parts in the system from the worn state to the failed state is the fifth failure rate, the failure rate of the non-failed parts in the system from the steady state to the failed state is the sixth failure rate, the fourth failure rateFifth failure rate->Sixth failure rate->Expressed as:
；
where n represents the total number of components in the system, γ represents a non-negative constant load factor, i represents the number of components in the system that are in a failure state, i=0, 1,2 …, n-k, k represents the number of at least operational components required for the system to function properly.
And calculating the transition intensity among all the system states in the first system state transition diagram according to the first system state transition diagram, the fourth failure rate, the fifth failure rate, the sixth failure rate and the number of parts of the system in a stable state and a wear state so as to obtain a first state transition intensity matrix. The system shown in fig. 4 is a schematic diagram of the state transition strengths associated with different states. The embodiment models the state transition process of the system by using the Markov process and considers the failure rate of transition among three periodic states of the component, so that the state transition diagram of the system can accurately describe the state transition process of the actual operation of the system.
According to the first state transition intensity matrix and by using a Chapman-Kolmogorov equation, calculating first probabilities that the system is in different system states at any moment. Is provided withSystem state a at time t ij Is a function related to the system runtime. The Chapman-Kolmogorov differential equation is constructed according to the first state transition intensity matrix and is:
；
wherein,expressed in timetThe system is in system state a (i-1)(j-1) Probability of->Expressed in timetThe system is in system state a i(j-1) Probability of->Expressed in timetThe system is in system state a (i-1)j Probability of->1 of the (n-j) steady state components are represented as having undergone a state transition,/->1 of the components representing (j-i) the wear state is subjected to a state transition,/->Representing that 1 of the (n-j+1) steady state components have undergone a state transition,/v>1 of the components representing the (j-i+1) wear states had a state transition.
In the one-step state transition in the first system state transition diagram, since the component has the characteristics of a steady state, a worn state, and a failed state, there are at most three possible transitions for the system to reach a certain state, and at most three possible transitions from that state, so the right side of the equation in the differential equation contains at most six terms, as shown in the differential equation above. And solving the differential equation by adopting a numerical method, and calculating to obtain the first probability that the system is in different system states at any moment.
Specifically, the above differential equations can be discussed in three general categories according to the difference between the values of i and j:
1. when i is less than or equal to n-k and i is less than j,
if i=0 and j+.n, the system is to reach state a ij From state a only i(j-1) The possibility of transfer is thus not included to the right of the differential equationAnd->Two terms, the differential equation, reduces to:
；
if i +.0 and j = n, the system is in state a ij Only transition to state a (i+1)j This possibility, the differential equation reduces to:
；
if i=0 and j=n, the system onlyCan be from state a i(j-1) Transition to state a ij This possibility, state a ij Transition to state a (i+1)j This possibility, the differential equation reduces to:
；
other cases in this condition are represented by the Chapman-Kolmogorov differential equation described above.
2. When i.ltoreq.n-k, and i=j
If i+.0, there are four transitions associated with this state, the differential equation reduces to:
；
if i=0, the system is in state a 00 There is no other state transition to state a 00 The differential equation reduces to:
。
3. when i=n-k+1
In this condition, the system is in a failure state and needs to stop working immediately, so that no state transition occurs, and two possible transitions exist to reach the failure state, and the differential equation is simplified as:
；
the initial values of the differential equation sets are set，/>And solving a differential equation by adopting a numerical method, and calculating to obtain the first probability that the system is in different system states at any moment.
And merging all the states of the systems in the first system state transition diagram into an absorption state, reconstructing the first system state transition diagram by using a Markov process to obtain a second system state transition diagram, accumulating the transition intensity from any one of the non-invalid system states in the second system state transition diagram to each invalid system state, and taking the accumulated sum as the transition intensity from the non-invalid system state to the absorption state, thereby obtaining the transition intensity from each non-invalid system state to the absorption state, and obtaining a second state transition intensity matrix.
Calculating a second probability function P of the system in an absorption state by using a Chapman-Kolmogorov equation F (t) according to a second probability function P F And (t) calculating a reliability function R (t) as follows:
；
by setting the reliability threshold D, the reliability function R (T) is calculated according to the R (T c ) When=d, the corresponding time T c ，T c The critical lifetime value of the system.
Will critical life T c Divided into N detection time intervals T IN After the completion of a detection time interval on the system, only when the system state is at time t m =mT IN Upon transition to state a ij In this case, since the checking operation is required, according to the first probability that the system is in a different system state at any time, the probability that the system needs to perform the detection at the mth detection time interval is:
；
wherein t is m-1 =(m-1)T IN ，t m =mT IN M represents an mth detection time interval,representing t m-1 Probability of being in state at the moment;
according to the probability of the system executing detection, the expected detection times of the system in the critical life are calculated as follows:
。
in order to calculate the runtime of a system in a non-absorbing state, it is necessary that the computing system reach state a before entering the absorbing state ij Is a function of the number of times desired. In the process of system state transition, from the first system state a 00 Initially in system state a ij Is calculated from the matrix N, wherein,
；
wherein I is an identity matrix, Q is a transient portion of a second state transition intensity matrix, and a first row of matrix N represents a state a of the system 00 Before starting to enter the absorption state, in the system state a ij To obtain the system in the system state a ij Is set to be a desired time E (T) ij ) The method comprises the following steps:
；
wherein N is ij Represented as system state slave a 00 Transfer to a ij Is a desired number of times;
the expected total run time E (T) of the system is:
。
the total cost of the system includes four different costs, namely, including the detection of the total cost C N Total cost of operation C OP Total cost of preventive maintenance C PM Total cost of corrective maintenance C CM . Total cost of operation C OP Associated with the full life cycle state of the component, i.e., with the operating costs of the component in steady state and worn state.
When the system is in state a ij (i.ltoreq.n-k) transportation per unit timeRunning costThe method comprises the following steps:
；
wherein c 2 Representing the running cost per unit time when the component is in steady state,c 1 indicating the running cost per unit time when the component is in a worn state,the running cost of the system in a non-failure state is obtained.
Total cost of operation C OP The sum of the expected time of each system state in each checking interval multiplied by the running cost of unit time under the system state is:
。
only when the system is in state a ij (i.ltoreq.n-k) before preventive maintenance activities need to be performed. When the system is in state a ij Preventive maintenance costs when (i.ltoreq.n-k)The method comprises the following steps:
；
wherein c PM Denoted as fixed cost of performing one preventive maintenance activity c r1 Expressed as the replacement costs of the individual parts in wear and tear conditions c r0 Expressed as replacement costs for a component in a failure state.
Total cost of preventive maintenance C PM Expressed as:
；
when the system is in the shapeState a ij (i=n-k+1) when the system is out of operation, corrective maintenance activities must be performed to re-operate the system. When the system is in state a ij Corrective maintenance costs at (i=n-k+1)The method comprises the following steps:
；
corrective maintenance total cost C CM The method comprises the following steps:
；
calculating the total cost of detection C based on the expected detection times E (IN) of the system IN the critical lifetime N Expressed as:
C N =E(IN)* C IN ；
wherein C is IN Representing the cost of each test;
the expected total operating cost of the system over the critical lifetime, E (C), is:
E(C)= C OP +C PM +C CM + C N 。
according to the expected total operation and maintenance cost E (C) and the expected total operation and maintenance time E (T) of the system, calculating to obtain the expected operation and maintenance cost CPT in the unit time of the system as follows:
；
it follows that the expected operation and maintenance cost CPT is related to the detection time interval T IN And a function of the detection times N, performing optimization model processing on the expected operation and maintenance cost CPT in unit time, wherein the optimization model is expressed as:
；
and carrying out optimizing algorithm processing on the optimizing model to obtain a detection time interval which enables the CPT to be minimum, wherein the detection time interval is the optimal detection time interval of the system, so that a better system maintenance strategy can be formulated. Aiming at the stable state, the abrasion state and the failure state of the component, different operation and maintenance cost, replacement cost and failure rate in unit time are considered, and the method is more in line with the actual engineering condition. Under the critical service life taking reliability as constraint, a preventive maintenance strategy based on inspection is formulated, so that the system can safely run in accordance with the reliability requirement, the operation and maintenance cost of the system can be reduced to the minimum, and the method has good engineering application value for predicting and health management of a k/n load balancing system.
As shown in fig. 5, the present application provides a method ofk/nA reliability evaluation and maintenance decision system of the load balancing system,k/nthe load balancing system consists of n identical components, the normal operation of k components ensures the normal operation of the system, and the reliability evaluation and maintenance decision system comprises:
the system state transition diagram module 51 is configured to define that the full life cycle states of the components include a stable state, a wear state and a failure state, determine the system state based on the full life cycle states of each component in the system, construct a first system state transition diagram according to failure rate and the system state during transition between the full life cycle states of the components, and calculate to obtain a first state transition intensity matrix, where the system state is used to represent the number of components in the wear state and the failure state in the system;
the probability calculation module 52 is configured to calculate, according to the first state transition intensity matrix and using the Chapman-Kolmogorov equation, a first probability that the system is in a different system state at any time;
the reliability calculation module 53 is configured to combine the states of all the systems in the first system state transition diagram that are in failure into an absorption state, construct a second state transition intensity matrix by using a markov process, calculate a second probability function of the system in the absorption state by using a Chapman-Kolmogorov equation, calculate a reliability function according to the second probability function, and obtain a critical lifetime of the system according to a preset reliability threshold;
the optimal model calculation module 54 is configured to calculate, according to the first probability, an expected total operation and maintenance cost and an expected total operation and maintenance time of the system in the critical lifetime, and calculate an expected operation and maintenance cost in a unit time of the system, so as to obtain an optimal detection time interval of the system.
Fig. 6 is a schematic hardware structure of a computer device according to an embodiment of the present application. The computer device shown in fig. 6 includes: processor 61, communication interface 62, memory 63 and communication bus 64, processor 61, communication interface 62, memory 63 accomplish each other's communication through communication bus 64. The connection manner between the processor 61, the communication interface 62, and the memory 63 shown in fig. 6 is merely exemplary, and in the implementation process, the processor 61, the communication interface 62, and the memory 63 may be communicatively connected to each other by other connection manners besides the communication bus 64.
The memory 63 may be used to store a computer program 631, the computer program 631 may include instructions and data to implement any of the abovek/nThe method comprises the steps of reliability evaluation and maintenance decision-making of the load balancing system. In the present embodiment, the memory 63 may be various types of storage media, such as random access memory (random access memory, RAM), read Only Memory (ROM), nonvolatile RAM (NVRAM), programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (electrical erasablePROM, EEPROM), flash memory, optical memory, registers, and the like. The storage 63 may include a hard drive and/or memory.
The processor 61 may be a general purpose processor, which may be a processor that performs certain steps and/or operations by reading and executing a computer program (e.g., computer program 631) stored in a memory (e.g., memory 63), which may use data stored in the memory (e.g., memory 63) in performing the steps and/or operations.
Communication interface 62 may include input/output (I/O) interfaces, physical interfaces, logical interfaces, and the like for implementing device interconnections within a network device, as well as interfaces for implementing network device interconnections with other devices (e.g., network devices). The communication network may be an ethernet, a radio access network (radio access network, RAN), a wireless local area network (wireless local areanetworks, WLAN), etc. The communication interface 62 may be a module, circuit, transceiver, or any device capable of communicating.
In implementation, the steps of the above method may be performed by integrated logic circuits of hardware in the processor 61 or by instructions in the form of software. The method disclosed in connection with the embodiments of the present application may be embodied directly in hardware processor execution or in a combination of hardware and software modules in a processor. The software modules may be located in a random access memory flash memory, read only memory, programmable read only memory, or electrically erasable programmable memory, registers, etc. as well known in the art. The storage medium is located in a memory 63 and the processor 61 reads the information in the memory 63 and in combination with its hardware performs the steps of the method described above. To avoid repetition, a detailed description is not provided herein.
Embodiments of the present application also provide a computer-readable storage medium having a computer program stored therein, the computer program implementing any of the above when executed by a processork/nA reliability evaluation and maintenance decision method for a load leveling system.
Although the preferred embodiments of the present application have been disclosed for illustrative purposes, those skilled in the art will appreciate that various modifications, additions and substitutions are possible, without departing from the scope and spirit of the application as disclosed in the accompanying claims.
Claims (10)
1. The method comprises the following steps ofk/nReliability assessment and maintenance decision for load leveling systemA policy method, saidk/nThe load balancing system consists of n identical components, wherein the normal operation of k components ensures the normal operation of the system, and the method is characterized by comprising the following steps:
s1, defining the total life cycle states of components to comprise a stable state, a wear state and a failure state, determining a system state based on the total life cycle states of all components in a system, constructing a first system state transition diagram according to failure rate and the system state during transition among all the total life cycle states of the components by using a Markov process, and calculating to obtain a first state transition intensity matrix, wherein the system state is used for representing the number of the components in the wear state and the failure state in the system;
s2, calculating first probabilities of different system states of the system at any moment according to the first state transition intensity matrix and by using a Chapman-Kolmogorov equation;
s3, combining all the states of the system in failure in the first system state transition diagram into an absorption state, constructing a second state transition intensity matrix by using a Markov process, calculating a second probability function of the system in the absorption state by using a Chapman-Kolmogorov equation, calculating a reliability function according to the second probability function, and obtaining the critical service life of the system according to a preset reliability threshold;
s4, calculating the expected total operation and maintenance cost and the expected total operation and maintenance time of the system in the critical service life according to the first probability, and calculating the expected operation and maintenance cost in the unit time of the system to obtain the optimal detection time interval of the system.
2. The method as claimed in claim 1k/nThe reliability evaluation and maintenance decision method of the load leveling system is characterized in that the step S1 comprises the following steps:
the system state is set to be denoted as a ij Wherein i is expressed as the number of components in a system in a failure state, and j is expressed as the total number of components in a failure state and a wear state;
setting the failure rate of the component from the steady state to the wearing state as the first failureEfficiency lambda 21 The failure rate of the component from the worn state to the failure state is the second failure rate lambda 10 The failure rate of the component from the steady state to the failure state is a third failure rate lambda 20 ；
When i parts fail in the system, the failure rate of the non-failed parts in the system from the stable state to the wear state is the fourth failure rate, the failure rate of the non-failed parts in the system from the wear state to the failure state is the fifth failure rate, the failure rate of the non-failed parts in the system from the stable state to the failure state is the sixth failure rate, the fourth failure rateFifth failure rate->Sixth failure rate->Expressed as:
；
where n represents the total number of components in the system, γ represents a non-negative constant load factor, i represents the number of components in the system that are in a failure state, i=0, 1,2 …, n-k;
and calculating the transition intensity among all the system states in the first system state transition diagram according to the first system state transition diagram, the fourth failure rate, the fifth failure rate, the sixth failure rate and the number of parts in a stable state and a wear state in the system so as to obtain a first state transition intensity matrix.
3. The method of claim 2k/nThe reliability evaluation and maintenance decision method of the load leveling system is characterized in that the step S2 comprises the following steps:
is provided withSystem state a at time t ij According to a first state transition intensity matrix, constructing a Chapman-Kolmogorov differential equation as follows:
；
wherein,expressed in timetThe system is in system state a (i-1)(j-1) Probability of->Expressed in timetThe system is in system state a i(j-1) Probability of->Expressed in timetThe system is in system state a (i-1)j Probability of->1 of the (n-j) steady state components are represented as having undergone a state transition,/->1 of the components representing (j-i) the wear state is subjected to a state transition,/->Representing that 1 of the (n-j+1) steady state components have undergone a state transition,/v>1 of the components representing the (j-i+1) wear states undergoes a state transition;
and solving the differential equation by adopting a numerical method, and calculating to obtain the first probability that the system is in different system states at any moment.
4. A method according to claim 3k/nThe reliability evaluation and maintenance decision method of the load leveling system is characterized in that the step S3 comprises the following steps:
combining all the states of the systems in the first system state transition diagram into an absorption state, reconstructing the first system state transition diagram by using a Markov process to obtain a second system state transition diagram, accumulating the transition intensities from any one of the non-invalid system states in the second system state transition diagram to each invalid system state, and taking the accumulated sum as the transition intensity from the non-invalid system state to the absorption state to obtain the transition intensity from each non-invalid system state to the absorption state, and obtaining a second state transition intensity matrix;
calculating a second probability function P of the system in an absorption state by using a Chapman-Kolmogorov equation F (t) according to a second probability function P F And (t) calculating a reliability function R (t) as follows:
。
5. as in claim 4k/nThe reliability evaluation and maintenance decision method of the load leveling system is characterized in that the step S4 includes:
will critical life T c Divided into N detection time intervals T IN According to the first probability that the system is in different system states at any moment, the probability that the system needs to execute detection at the mth detection time interval is as follows:
；
wherein t is m-1 =(m-1)T IN ，t m =mT IN M represents an mth detection time interval,representing t m-1 The time system is in statea 00 Probability of (2);
according to the probability of the system executing detection, calculating to obtain the expected detection times of the system in the critical service life as follows;
；
in the process of system state transition, from the first system state a 00 Initially in system state a ij Is calculated from the matrix N, wherein,
；
wherein I is an identity matrix, Q is a transient portion of a second state transition intensity matrix, and a first row of matrix N represents a state a of the system 00 Before starting to enter the absorption state, in the system state a ij Is a desired number of times;
the system is in system state a ij Is set to be a desired time E (T) ij ) The method comprises the following steps:
，
wherein N is ij Represented as system state slave a 00 Transfer to a ij Is a desired number of times;
the expected total run time E (T) of the system is:
。
6. as in claim 5k/nThe reliability evaluation and maintenance decision method of the load leveling system is characterized in that the step S4 includes:
when the system is in state a ij (i≤n-k) running cost per unit timeThe method comprises the following steps:
；
wherein c 2 Representing the running cost per unit time when the component is in steady state,c 1 representing the running cost per unit time when the component is in a worn state;
total cost of operation C OP The sum of the expected time for each system state within each inspection interval multiplied by the running cost per unit time for that system state is expressed as:
。
7. the method as claimed in claim 6k/nThe reliability evaluation and maintenance decision method of the load leveling system is characterized in that the step S4 includes:
when the system is in state a ij Preventive maintenance costs when (i.ltoreq.n-k)The method comprises the following steps:
；
wherein c PM Denoted as fixed cost of performing one preventive maintenance activity c r1 Expressed as replacement cost of a worn part, c r0 Denoted as replacement cost of a component in a failure state;
total cost of preventive maintenance C PM Expressed as:
。
8. the method as claimed in claim 7k/nThe reliability evaluation and maintenance decision method of the load leveling system is characterized in that the step S4 includes:
when the system is in state a ij Corrective maintenance costs at (i=n-k+1)The method comprises the following steps:
；
corrective maintenance total cost C CM The method comprises the following steps:
；
calculating the total cost of detection C based on the expected detection times E (IN) of the system IN the critical lifetime N Expressed as:
C N =E(IN)* C IN ；
wherein C is IN Representing the cost of each test;
the expected total operating cost of the system over the critical lifetime, E (C), is:
E(C)= C OP +C PM +C CM + C N 。
9. the method as claimed in claim 8k/nThe reliability evaluation and maintenance decision method of the load leveling system is characterized in that the step S4 includes:
according to the expected total operation and maintenance cost E (C) and the expected total operation and maintenance time E (T) of the system, calculating to obtain the expected operation and maintenance cost CPT in the unit time of the system as follows:
；
carrying out optimization model processing on expected operation and maintenance cost CPT in unit time, wherein the optimization model is expressed as:
；
and carrying out optimization algorithm processing on the optimization model to obtain a detection time interval for minimizing the CPT, wherein the detection time interval is the optimal detection time interval of the system.
10. The method comprises the following steps ofk/nReliability assessment and maintenance decision system for load leveling system, said systemk/nThe load balancing system consists of n identical components, and k components work normally to ensure the system to work normally, and is characterized in that the reliability evaluation and maintenance decision system comprises;
the system state transition diagram module is used for defining the full life cycle states of the components, including a stable state, a wear state and a failure state, determining the system state based on the full life cycle states of all the components in the system, constructing a first system state transition diagram according to failure rate and the system state when the full life cycle states of the components are transitioned, and calculating to obtain a first state transition intensity matrix, wherein the system state is used for representing the number of the components in the wear state and the failure state in the system;
the probability calculation module is used for calculating the first probability of the system in different system states at any moment according to the first state transition intensity matrix and by using a Chapman-Kolmogorov equation;
the reliability calculation module is used for combining all the states of the systems in the first system state transition diagram in failure into an absorption state, constructing a second state transition intensity matrix by using a Markov process, calculating a second probability function of the systems in the absorption state by using a Chapman-Kolmogorov equation, calculating a reliability function according to the second probability function, and obtaining the critical service life of the system according to a preset reliability threshold;
and the optimal model calculation module is used for calculating the expected total operation and maintenance cost and the expected total operation and maintenance time of the system in the critical service life according to the first probability, and calculating the expected operation and maintenance cost in the unit time of the system so as to obtain the optimal detection time interval of the system.
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