A reliability optimization method for load sharing system based on gamma process

Abstract

The present invention relates to a reliability optimization method for a load sharing system based on a gamma process, and belongs to the field of automatic control technology. The present invention is aimed at a load sharing method in which component performance degradation obeys a gamma process, and proposes a method for calculating a load distribution coefficient based on average remaining life. The system is evaluated by the reliability function at the next detection moment. Compared with the traditional load average distribution mode, the life and reliability of the load sharing system can be effectively improved. The method proposed by the present invention requires less theoretical knowledge, is simple to calculate, easy to implement, and is convenient for engineering and technical personnel to master and use.

Description

Technical Field

[0001] The invention relates to a reliability optimization method for a load sharing system based on a gamma process, and belongs to the technical field of automatic control. Background Art

[0002] Load sharing mechanism is a common means to improve system reliability and has been widely used in many engineering practices. In the load sharing system, all components share the entire load, and the load of the failed component will be distributed to the components that have not failed according to a certain rule. Figure 1 As shown in the figure, at the beginning of operation, the total load L is shared by the two components of the load sharing system, among which the load bearing ratio of component 1 is 0≤λ≤1, which is also called the load sharing coefficient of the system. Therefore, the loads borne by the two components are L1=λL, L2=(1-λ)L. After any component fails, the load it bears is redistributed to another component that has not failed, until the component also fails, and the entire load sharing system fails.

[0003] In a load-sharing system, the performance degradation and reliability evolution of each component are inevitably affected by the size of the shared load, and the component load is determined by the load distribution mode, that is, the value of the load sharing coefficient λ. Existing research and applications are mainly based on the traditional load average distribution mode, which assumes that the load size shared by all components is equal. When a component fails, its load will be evenly distributed to all surviving components. In fact, due to individual differences between components and the heterogeneity of the working environment, the components of the load-sharing system are often in different degradation states and reliability levels after working for the same time. Therefore, the commonly used load average distribution mode cannot best balance the performance degradation and reliability change process between different components, and the life and reliability of the entire load-sharing system can be further optimized and improved.

[0004] To this end, the present invention provides a load sharing system reliability optimization method based on a gamma process. Summary of the invention

[0005] The invention provides a load sharing system reliability optimization method based on a gamma process.

[0006] The specific steps are as follows:

[0007] Step 1: Modeling the component performance degradation process

[0008] Consider a load sharing system consisting of two components. The degradation process of each component follows a gamma process, that is, the increment follows an independent gamma distribution. Let x i (Δt) is the degradation of component i in Δt time, then x i (Δt) satisfies:

[0009] ①x i (0) = 0, and x i (Δt) is continuous at Δt = 0;

[0010] ② In any non-intersecting time period, the degradation amounts are independent of each other. For example, if Δt1 and Δt2 do not intersect, then x i (Δt1), x i (Δt2), independent of each other;

[0011] ③x i (Δt) follows the gamma distribution Gamma(α i Δt, β i ), its probability density function is:

[0012]

[0013] Among them, α i It is a shape parameter that characterizes the working stress of the product and is related to the load shared by the components; β i It is a scalar parameter that reflects the failure mechanism of the product and has nothing to do with the load shared by the component;

[0014] is the gamma function;

[0015] Assume that the shape parameter α of the degradation model of component i (i=1,2) is i The load L i It can be described by the inverse power law model, that is, Among them A i >0,c i >0 is a constant;

[0016] If component i (i=1,2) is at the current detection time t k The performance degradation is x i , whose failure threshold is D i , then at the next detection time t k+1 The reliability can be expressed as follows:

[0017]

[0018] Where Δt = t k+1 -t k To detect the time interval, is the time interval (t k , t k+1 ) within the degradation increment.

[0019] Step 2: Calculation of system load distribution coefficient

[0020] Since component i is in the time interval [tk , t k+1 The degenerate increment in ] follows the gamma distribution, that is, The average remaining life of component i is:

[0021]

[0022] Since the average remaining life of a component reflects both the current performance degradation level of the component and the average rate of the component in the future degradation process, and this rate is related to the load shared by the component, in order to balance the degradation difference and degradation rate between components, with the goal of equalizing the average remaining life of the two components, the following equation is established:

[0023] E(RUL1)=E(RUL2)

[0024]

[0025]

[0026] By solving the above equation, we can get the new system load distribution coefficient λ * .

[0027] Step 3: System reliability assessment and optimization

[0028] After obtaining the new system load distribution coefficient λ * After that, the reliability model of the load sharing system can be established.

[0029] Based on the two components at the current detection time t k From the performance degradation, we can know that the system is still fault-free at the next detection moment, which can be divided into three cases: neither component fails, component 1 fails but component 2 does not fail, component 2 fails but component 1 does not fail. Combining these three cases, we can get the reliability function of the system.

[0030] ④ Both components are not faulty:

[0031]

[0032] ⑤ Component 1 is faulty and component 2 is not faulty:

[0033]

[0034] Where f1(s) represents the probability density function of component 1 at failure time s, which can be approximated by BS distribution:

[0035]

[0036] And Δx 2(k，s) and Δx 2(s，k+1) The parameters are respectively and The gamma distribution of Δx is known from the additivity of the gamma distribution. 2(k，s) +Δx 2(s，k+1) The obedience parameters are Gamma distribution, so we have:

[0037]

[0038] in, is the incomplete gamma function.

[0039] ⑥ Component 2 is faulty and component 1 is not faulty:

[0040]

[0041] Where f2(w) represents the probability density function of component 2 at failure time w, which can be approximated by BS distribution:

[0042]

[0043] And Δx 1(k，2) and Δx 1(w，k+1) The parameters are respectively and The gamma distribution of Δx is known from the additivity of the gamma distribution. 1(k，s) +Δx 1(s，k+1) The obedience parameters are Gamma distribution, so we have:

[0044]

[0045] Combining the above three situations, we can obtain the load sharing system at t k+1 Reliability at all times:

[0046] R S (t k+1 )=R S1 (t k+1 )+R S2 (t k+1 )+R S3 (t k+1 ).

[0047] The reliability optimization method of a load sharing system based on a gamma process of the present invention has the following advantages:

[0048] The present invention proposes a method for calculating the load distribution coefficient based on the average remaining life for a load sharing method in which the performance degradation of components follows the gamma process. The method is evaluated by the reliability function of the system at the next detection moment. Compared with the traditional load average distribution mode, the life and reliability of the load sharing system can be effectively improved. The method proposed by the present invention requires less theoretical knowledge, is simple to calculate, easy to implement, and is convenient for engineering and technical personnel to master and use. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 , Schematic diagram of the load sharing system of the two components. DETAILED DESCRIPTION

[0050] A load sharing method based on a gamma process comprises the following steps:

[0051] Step 1: Modeling the component performance degradation process

[0052] Consider a load sharing system consisting of two components. The degradation process of each component follows a gamma process, that is, the increment follows an independent gamma distribution. Let x i (Δt) is the degradation of component i in Δt time, then x i (Δt) satisfies:

[0053] ①x i (0) = 0, and x i (Δt) is continuous at Δt = 0;

[0054] ② In any non-intersecting time period, for example, Δt1 and Δt2 do not intersect, then x i (Δt1), x i (Δt2), independent of each other;

[0055] ③x i (Δt) follows the gamma distribution Gamma(α i Δt, β i ), its probability density function is:

[0056]

[0057] Among them, α i It is a shape parameter that characterizes the working stress of the product and is related to the load shared by the components; β i It is a scalar parameter that reflects the failure mechanism of the product and has nothing to do with the load shared by the component;

[0058] is the gamma function;

[0059] Assume that the shape parameter α of the degradation model of component i (i=1,2) is i The load Li It can be described by the inverse power law model, that is, Among them A i >0,c i >0 is a constant;

[0060] If component i (i=1,2) is at the current detection time t k The performance degradation is x i , whose failure threshold is D i , then at the next detection time t k+1 The reliability can be expressed as follows:

[0061]

[0062] Where Δt = t k+1 -t k To detect the time interval, is the time interval (t k , t k+1 ) within the degradation increment.

[0063] Step 2: Calculation of system load distribution coefficient

[0064] Since component i is in the time interval [t k , t k+1 The degenerate increment in ] follows the gamma distribution, that is, The average remaining life of component i is:

[0065]

[0066] Since the average remaining life of a component reflects both the current performance degradation level of the component and the average rate of the component in the future degradation process, and this rate is related to the load shared by the component, in order to balance the degradation difference and degradation rate between components, with the goal of equalizing the average remaining life of the two components, the following equation is established:

[0067] E(RUL1)=E(RUL2)

[0068]

[0069]

[0070] By solving the above equation, we can get the new system load distribution coefficient λ * .

[0071] Taking a certain ship power system as an example, the present invention is described in detail.

[0072] The power system of a ship consists of two subsystems, which jointly undertake the power output task. The total power load L = 1, and the power output tasks undertaken by the two subsystems are L1 = λL = λ, L2 = (1-λ)L = 1-λ. Assume that the performance degradation of the two subsystems obeys the gamma process model. k The model parameters at the moment =1 are shown in the following table.

[0073] Table 1 Parameters of the subsystem performance degradation model of a ship power system

[0074]

[0075] To evaluate the dynamic system at t k+1 =2 time reliability, the present invention provides a load sharing system reliability optimization method based on the gamma process, and the specific implementation steps are as follows:

[0076] Step 1: Modeling the component performance degradation process.

[0077] Based on the subsystem performance degradation model parameters of the power system in Table 1, subsystem 1 and subsystem 2 can be divided into k+1 =2 The reliability functions at the moment are:

[0078]

[0079]

[0080] Step 2: Calculation of system load distribution coefficient.

[0081] By solving the equation

[0082] E(RUL1)=E(RUL2)

[0083] 15λ -1.5 =8(1-λ) -1.5

[0084] The new system load distribution coefficient λ can be obtained * =0.3967.

[0085] Step 3: System reliability assessment and optimization.

[0086] The calculated load distribution factor λ * Substituting the performance degradation model and reliability function of the two-part system, the reliability function of a ship power system at time t is derived based on the following three situations.

[0087] ① There is no failure in both systems:

[0088] R S1 (t k+1 )=R1(t k+1)*R2(t k+1 )=0.431

[0089] ② Component 1 is faulty and component 2 is not faulty:

[0090]

[0091] ③ Component 2 is faulty and component 1 is not faulty:

[0092]

[0093] Combining the above three situations, we can obtain the power system of a ship at t k+1 Reliability at all times:

[0094] R S (t k+1 )=R S1 (t k+1 )+R S2 (t k+1 )+R S3 (t k+1 )=0.741

[0095] Compared with the system reliability under the load average distribution mode, it is calculated that when α = 0.5, the power system of a certain ship is k+1 The reliability of the moment is:

[0096] R0(t k+1 )=0.728

[0097] It can be seen that compared with the load average distribution mode, under the proposed load distribution coefficient based on the average remaining life, the power system of a certain ship is k+1 The reliability improvement ratio at the moment is

[0098]

Claims

1. A method for optimizing the reliability of a load sharing system based on a gamma process, characterized in that: The specific steps are as follows: Step 1: Modeling the component performance degradation process Consider a load sharing system consisting of two components. The degradation process of each component follows a gamma process. Let x i (Δt) is the degradation of component i in Δt time, then x i (Δt) satisfies: ①x i (0) = 0, and x i (Δt) is continuous at Δt = 0; ② The degradation amounts are independent of each other in any non-overlapping time periods; ③x i (Δt) follows the gamma distribution Gamma(α i Δt, β i ), its probability density function is: Among them, α i It is a shape parameter that characterizes the working stress of the product and is related to the load size shared by the components; β i It is a scalar parameter that reflects the failure mechanism of the product and has nothing to do with the load shared by the component; is the gamma function; Shape parameter α of the degradation model for component i, i=1,2 i The load L i It can be described by the inverse power law model, that is, Among them A i >0,c i >0 is a constant; Component i, i=1, 2 at the current detection time t k The performance degradation is x i , whose failure threshold is D i , then at the next detection time t k+1 The reliability is expressed as follows: Where Δt = t k+1 -t k To detect the time interval, is the time interval (t k , t k+1 ) within the degradation increment; Step 2: Calculation of system load distribution coefficient Since component i is in the time interval [t k , t k+1 The degenerate increment in ] follows the gamma distribution, that is, The average remaining life of component i is: Since the average remaining life of a component reflects both the current performance degradation level of the component and the average rate of the component in the future degradation process, and this rate is related to the load shared by the component, in order to balance the degradation difference and degradation rate between components, with the goal of equalizing the average remaining life of the two components, the following equation is established: E(RUL1)=E(RUL2) By solving the above equation, we can get the new system load distribution coefficient λ * ; Step 3: System reliability assessment and optimization After obtaining the new system load distribution coefficient λ * After that, the reliability model of the load sharing system can be established; Based on the two components at the current detection time t k From the performance degradation, we can know that the system still has no fault at the next detection time, which can be divided into three cases: neither of the two components fails, component 1 fails but component 2 does not fail, component 2 fails but component 1 does not fail. Combining these three cases, we can get the reliability function of the system. ① Both components are not faulty: ② Component 1 is faulty and component 2 is not faulty: Where f1(s) represents the probability density function of component 1 at failure time s, which can be approximated by BS distribution: And Δx 2(k，s) and Δx 2(s，k+1) The parameters are respectively and The gamma distribution of Δx is known from the additivity of the gamma distribution. 2(k，s) +Δx 2(s，k+1) The obedience parameters are Gamma distribution, so we have: in, is the incomplete gamma function; ③ Component 2 is faulty and component 1 is not faulty: Where f2(w) represents the probability density function of component 2 at failure time w, which can be approximated by BS distribution: And Δx 1(k，2) and Δx 1(w，k+1) The parameters are respectively and The gamma distribution of Δx is known from the additivity of the gamma distribution. 1(k，s) +Δx 1(s，k+1) The obedience parameters are Gamma distribution, so we have: Combining the above three situations, we can obtain the load sharing system at t k+1 Reliability at all times: R S (t k+1 )=R S1 (t k+1 )+R S2 (t k+1 )+R S3 (t k+1 )。

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