A reliability assessment method, system, device and medium for a competitive failure system considering the self-healing effect of impact damage

Abstract

The present invention discloses a reliability assessment method, system, device and medium for a competing failure system that takes into account the self-healing effect of impact damage, and relates to the technical field of reliability assessment for competing failure systems. The method comprises: calculating the probability that a system will not experience degradation failure based on degradation modeling theory; based on a cumulative impact damage model, using the probability that the system will not experience degradation failure to derive the probability that the system will not experience impact failure under two conditions, considering the damage self-healing effect and not considering the damage self-healing effect; based on the "degradation-threshold-impact" theory, using the probability that the system will not experience degradation failure and the probability that the system will not experience impact failure to derive the reliability function of the system; the reliability function is used to perform reliability assessment for a competing failure system that takes into account the self-healing effect of impact damage. The present invention can improve the accuracy of reliability assessment by constructing a more generalized component-level related competing failure process reliability evaluation model.

Description

Technical Field

[0001] The present invention relates to the technical field of reliability assessment of competing failure systems, and in particular to a reliability assessment method, system, equipment and medium for a competing failure system considering the self-healing effect of impact damage. Background Art

[0002] Failure modes in complex systems can be categorized as degradation failure and shock failure. On the one hand, system performance degrades over time. If the degradation exceeds the degradation failure threshold, the system fails. On the other hand, shock failure can occur at any time, leading to complete loss of system functionality. Shock failure can occur due to external shocks (such as electrical shocks and thermal shocks) exceeding the system's shock failure threshold, or due to insufficient system performance (such as strength and stiffness).

[0003] If both degradation failure and shock failure occur simultaneously during system operation, the system's ultimate failure is the result of competition between these two failure modes. Therefore, competing failure theory is more suitable for describing reliability analysis of systems with multiple failure modes. Furthermore, degradation failure and sudden failure in a product are often not independent but rather correlated. For example, pulsed xenon lamp failures typically include degradation failures caused by melting and evaporation of the electrode material and sudden failures caused by lamp explosion, with the probability of lamp explosion decreasing with the degree of product degradation.

[0004] Previous studies have assumed that damage caused by shock to a system is irreversible, meaning that remediating the damage requires external repair resources. In 2001, American scientists White et al., building on the concept of a passive embedded self-repair system, first proposed a microcapsule-embedded polymer self-repair model. The repair process of microcapsule self-healing materials is as follows: when a crack in the substrate propagates and ruptures the microcapsule, the repair agent in the microcapsule flows to the crack under capillary action, where it undergoes a polymerization reaction under the action of a catalyst, repairing the crack. In the nearly two decades since then, research on self-healing materials has rapidly advanced, attracting widespread attention in fields such as engineering, defense, offshore oil exploration, electronics, and biomedicine.

[0005] Self-healing materials possess the ability to heal and repair themselves, generally without the need for external maintenance intervention. For example, tiny cracks on a spacecraft's hull often appear beneath the material, hidden from the human eye. Once formed, these cracks continue to expand, weakening the material's resistance until it eventually breaks. To prevent these cracks from expanding, scientists have developed a new material that can detect damage and instantly repair itself, extending the lifespan of spacecraft. Furthermore, concrete infused with a special healing agent can automatically generate limestone upon contact with water, helping cracks in walls heal automatically and extending the lifespan of buildings without manual repair. Smart materials used in protective applications can detect issues such as coating thickness or particle concentration levels that fall below standard, and then respond with novel responses to these changes for repair, eliminating manual maintenance. Therefore, a reliability assessment method for competing failure systems involving these new materials is urgently needed. Summary of the Invention

[0006] The purpose of the present invention is to provide a method, system, equipment and medium for reliability assessment of a competing failure system taking into account the self-healing effect of impact damage, which can improve the accuracy of reliability assessment by constructing a more generalized component-level related competing failure process reliability evaluation model.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A reliability assessment method for a competing failure system considering the self-healing effect of impact damage includes:

[0009] Based on degradation modeling theory, the probability that the system will not experience degradation failure is calculated;

[0010] Based on the cumulative impact damage model, the probability of the system not experiencing degradation failure is used to derive the probability of the system not experiencing impact failure under two conditions: with and without considering the damage self-healing effect.

[0011] Based on the "degradation-threshold-impact" theory, the reliability function of the system is derived using the probability that the system will not experience degradation failure and the probability that the system will not experience impact failure. The reliability function is used to perform reliability assessment of the competing failure system considering the self-healing effect of impact damage.

[0012] Optionally, the calculation process of the probability that the system does not suffer degradation failure is:

[0013] The Gamma process is introduced to describe the system degradation process:

[0014] The system starts running at the initial time t = 0 in the best state. The internal degradation amount X(t) obeys the Gamma distribution with shape parameters αt and scale parameters β, respectively. We get X(t) ~ gamma(αt, β), and the probability density function is:

[0015]

[0016] Where 1(x≥0) is the indicator function, Γ is the Gamma function, and

[0017] The distribution function of the internal degradation amount is:

[0018]

[0019] Where Γ(a, z) is an incomplete Gamma function, and The mean and variance of X(t) are E[X(t)] = αt / β and Var[X(t)] = αt / β respectively. 2 ;

[0020] Further derive the probability that the system does not experience degradation failure:

[0021] For the related competition failure system, the jth (j=1,2,…,|φ i |) the affected shock types with intensity λ ij (t) is a nonhomogeneous Poisson process {N ii (t), t≥0} arrives, the damage amount of the jth effective impact type acting on the system is Y ij1 , Y ij2 ,…,Y ij1 , Y ij2 , ...are independent of each other and obey the same distribution, and the distribution function is:

[0022]

[0023] The total performance degradation of the system S i (t) is expressed as:

[0024]

[0025] Total performance degradation S i The distribution of (t) is:

[0026]

[0027]

[0028] in, express The n-order Stieltjes convolution of , therefore, the probability that the system does not fail within time t is:

[0029]

[0030] Let X i Represents X i (t) is the realization of discretization at time t, denoted by Z i =X i -X i-1 ; Assume that Z1, Z2, ... are independent and identically Gamma distributed random variables with shape parameters α and scale parameters β respectively, and N is X i The discretization of (t) is realized by X i The first time it reaches x, the probability of at least N shocks occurring within time n is:

[0031] P{N≥n}=P{X i ≤x}

[0032] Due to X i =Z1+Z2+…+Z i , according to the central limit theorem, we have:

[0033]

[0034] The continuous implementation of N is achieved by the Birnbaum-Saunders distribution Expressed as i >>1, Gamma distribution X i Reasonably approximated by the Inverse Gaussian distribution, assuming that Y ijk Obey the mean The variance is The probability that the system does not fail due to degradation is:

[0035]

[0036] Optionally, the probability of the system not experiencing impact failure without considering the damage self-healing effect is:

[0037] When the self-healing effect of damage is not considered, the impact damage amount W that causes impact failure is ij1 , W ij2 , ... does not change with time t and number of shocks N ij (t) changes, cumulative impact damage W i The distribution of (t) is:

[0038]

[0039] Assume W ijkObey the mean The variance is The cumulative impact damage that leads to impact failure is The probability that the system does not experience shock failure is:

[0040] R i，HF (t) = P{W i (t) <D i}

[0041]

[0042] Among them, D i is the impact failure threshold; m j is the number of external shocks; ij is a function of the intensity of each impact.

[0043] Optionally, the probability of no impact failure of the system taking into account the damage self-healing effect is:

[0044] When considering the damage self-healing effect, the impact damage amount W that causes impact failure ij1 , W ij2 , ...is reduced to W at time t ijk exp[-γ(N ij (t)-k)], cumulative impact damage W i The distribution of (t) is:

[0045]

[0046] Assume W ijk Obey the mean The variance is The normal distribution of the impact damage that leads to impact failure is W i (t) also obeys the normal distribution, and its mean is:

[0047]

[0048]

[0049] The variance is:

[0050]

[0051] The probability that the system does not experience shock failure is:

[0052]

[0053] Where γ (γ>0) is the introduced damage self-healing coefficient; D i is the impact failure threshold; m jis the number of external shocks; ij is a function of the intensity of each impact.

[0054] Optionally, the derivation process of the reliability function is:

[0055] After obtaining the probability that the system will not experience degradation failure and shock failure, the general form of the system reliability function is obtained according to the type of shock affected:

[0056]

[0057]

[0058] Assume that the mth (m=1, 2, ..., M) impact type has a strength of λ m The inhomogeneous Poisson process of (t) arrives and is independent of other shock types until the number of arrivals at time t is n m , then the general form of the system reliability function is:

[0059]

[0060] Among them, W i (t) is the cumulative impact damage that leads to impact failure.

[0061] The present invention also provides a reliability assessment system for a competitive failure system taking into account the self-healing effect of impact damage, comprising:

[0062] A calculation unit, used to calculate the probability that the system will not fail due to degradation based on degradation modeling theory;

[0063] A derivation unit is used to derive the probability of the system not failing due to impact under two conditions, one with and the other without considering the damage self-healing effect, based on the cumulative impact damage model and using the probability of the system not failing due to degradation;

[0064] A reliability function construction unit is used to derive the reliability function of the system based on the "degradation-threshold-impact" theory using the probability that the system will not fail due to degradation and the probability that the system will not fail due to impact; the reliability function is used to perform reliability assessment of the competing failure system considering the self-healing effect of impact damage.

[0065] The present invention also provides an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the above-mentioned competitive failure system reliability assessment method considering the self-healing effect of impact damage.

[0066] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the reliability assessment method for a competing failure system considering the self-healing effect of impact damage as described above.

[0067] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0068] The present invention discloses a reliability assessment method, system, device, and medium for a competing failure system that considers the self-healing effect of impact damage. The method includes calculating the probability of the system not experiencing degradation failure based on degradation modeling theory; using the cumulative impact damage model, deriving the probability of the system not experiencing impact failure using the probability of no degradation failure, both when considering the damage self-healing effect and when not considering the damage self-healing effect; and deriving the system's reliability function based on the "degradation-threshold-impact" theory using the probability of no degradation failure and the probability of no impact failure. The reliability function is used to perform reliability assessment of a competing failure system that considers the self-healing effect of impact damage. The present invention improves the accuracy of reliability assessment by constructing a more generalized component-level reliability evaluation model for related competing failure processes. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0070] Figure 1 Schematic diagram of the process of the reliability assessment method of the competitive failure system of the present invention;

[0071] Figure 2 Schematic diagram of the system degradation failure process in this embodiment;

[0072] Figure 3 This is a schematic diagram of the system impact failure process when the self-healing effect of impact damage is not considered in this embodiment;

[0073] Figure 4 This is a schematic diagram of the system impact failure process when the impact damage self-healing effect is considered in this embodiment. DETAILED DESCRIPTION

[0074] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0075] The purpose of the present invention is to provide a method, system, equipment and medium for reliability assessment of a competing failure system taking into account the self-healing effect of impact damage, which can improve the accuracy of reliability assessment by constructing a more generalized component-level related competing failure process reliability evaluation model.

[0076] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0077] like Figure 1 As shown, the present invention provides a reliability assessment method for a competitive failure system considering the self-healing effect of impact damage, comprising:

[0078] Step 100: Calculate the probability that the system will not experience degradation failure based on degradation modeling theory;

[0079] Step 200: Based on the cumulative impact damage model, the probability of the system not experiencing degradation failure is used to derive the probability of the system not experiencing impact failure under two conditions: considering the damage self-healing effect and not considering the damage self-healing effect.

[0080] Step 300: Based on the “degradation-threshold-impact” theory, the reliability function of the system is derived using the probability that the system will not experience degradation failure and the probability that the system will not experience impact failure. The reliability function is used to perform reliability assessment of the competing failure system considering the self-healing effect of impact damage.

[0081] Based on the above technical solution, each step is further elaborated in detail.

[0082] The specific content of step 100 is as follows:

[0083] (1) Introduce the Gamma process to describe the system degradation process, such as Figure 2 shown.

[0084] The system starts running at the initial time t = 0 in the best state. The internal degradation amount X(t) obeys the Gamma distribution with shape parameters αt and scale parameters β, that is, X(t) ~ gamma(αt, β). Its probability density function is:

[0085]

[0086] Where 1(x≥0) is the indicator function, Γ is the Gamma function, and

[0087] The distribution function of the internal degradation amount X(t) is:

[0088]

[0089] Where Γ(a, z) is an incomplete Gamma function, and The mean and variance of X(t) are E[X(t)] = αt / β and Var[X(t)] = αt / β respectively. 2 .

[0090] (2) Derivation of the probability that the system will not fail due to degradation

[0091] There are many types of external shocks and the external shocks only increase the current degradation amount, do not change the degradation rate, that is, do not affect the values ​​of the parameters α and β related to the degradation rate. For the related competitive failure system, it is j (j = 1, 2, ..., |φ i |) the affected shock types with intensity λ ij (t) is a nonhomogeneous Poisson process {N ij (t), t≥0} arrives. The damage amount of the jth effective impact type acting on the system is Y ij1 , Y ij2 ,…,Y ij1 , Y ij2 , ...are independent of each other and obey the same distribution, and the distribution function is:

[0092]

[0093] The total performance degradation of the system S i (t) can be expressed as:

[0094]

[0095] Total performance degradation S i The distribution of (t) is:

[0096]

[0097] in, express Therefore, the probability that the system does not fail within time t is:

[0098]

[0099] Although the exact probability of the system not experiencing degradation failure can be obtained, its analytical solution is difficult to obtain directly due to the existence of convolution. Here, the approximate calculation is performed by using the Gamma distribution to approximate the normal distribution.

[0100] Let X i Represents X i (t) is a realization of discretization at time t, denoted by Z i =X i -X i-1 Assume that Z1, Z2, ... are independent and identically Gamma distributed random variables with shape parameters α and scale parameters β respectively, and N is X i The discretization of (t) is realized by X i The first time it reaches x, the probability of at least N shocks occurring within time n is:

[0101] P{N≥n}=P{X i ≤x}

[0102] Due to X i =Z1+Z2+…+Z i , according to the central limit theorem, we have:

[0103]

[0104] The continuous realization of N can be achieved by Birnbaum-Saunders distribution To express it, and when α>>1, the Gamma distribution X i It can be reasonably approximated by the Inverse Gaussian distribution. Assume that Y ijk Obey the mean The variance is The probability that the system does not fail due to degradation is:

[0105]

[0106]

[0107] The specific content of step 200 is as follows:

[0108] The impact of the system increases the current performance degradation on the one hand, and may cause the system to fail on the other hand. i The amount of damage caused by each impact type is W. ij1 , W ij2 ,….W ij1 , W ij2 , ...are independent of each other and obey the same distribution, and the distribution function is:

[0109]

[0110] As a generalization of the standard cumulative impact damage model, this step analyzes the probability that the system does not fail due to impact when the damage self-healing effect is considered and the probability that the system does not fail due to impact when the damage self-healing effect is not considered. Figure 3 is the standard cumulative impact damage model, that is, the impact damage amount W that causes impact failure ij1 , W ij2 , ... does not change with time t and number of shocks N ij (t)Change. Figure 4 It is an extended cumulative impact damage model that considers the self-healing ability of the damage of the internal components of the system. The impact damage amount W that leads to impact failure is ij1 , W ij2 , ...with time t and number of shocks N ij (t) gradually decreases. Specifically, from the jth (j = 1, 2, ..., |φ i |) the kth (k=1,2,…,N) type of shock ij (t)) Impact damage W ijk At time t, it is reduced to W ijk exp[-γ(N ij (t)-k)], where γ (γ>0) is the introduced damage self-healing coefficient.

[0111] (1) The probability that the system does not experience shock failure when the damage self-healing effect is not considered

[0112] Without considering the self-healing effect of damage, the impact damage amount W that causes impact failure is ij1 , W ij2 , ... does not change with time t and number of shocks N ij (t) changes. Cumulative impact damage W i The distribution of (t) is:

[0113]

[0114]

[0115] Assume W ijk Obey the mean The variance is The cumulative impact damage that leads to impact failure is The probability that the system does not experience shock failure is:

[0116]

[0117] (2) The probability that the system does not experience shock failure when considering the damage self-healing effect

[0118] When considering the damage self-healing effect, the impact damage amount W that causes impact failure is ij1 , W ij2 , ...is reduced to W at time t ijk exp[-γ(N ij (t)-k)]. Cumulative impact damage W i The distribution of (t) is:

[0119]

[0120]

[0121] Assume W ijk Obey the mean The variance is The normal distribution of the impact damage that leads to impact failure is W i (t) also obeys the normal distribution, and its mean is:

[0122]

[0123] The variance is:

[0124]

[0125] The probability that the system does not experience shock failure is:

[0126]

[0127] The specific content of step 300 is as follows:

[0128] After obtaining the probability that the system will not experience degradation failure and shock failure, the general form of the system reliability function can be obtained according to the shock type it is affected by:

[0129]

[0130] Assume that the mth (m=1, 2, ..., M) impact type has a strength of λ m The inhomogeneous Poisson process of (t) arrives and is independent of other shock types until the number of arrivals at time t is n m , then the general form of the system reliability function is:

[0131]

[0132] Therefore, inspired by the self-healing ability of special materials, this paper introduces a damage self-healing coefficient to expand the standard cumulative impact damage model for the impact failure process in a related competing failure system. This paper proposes a reliability assessment method for competing failure systems that considers the impact damage self-healing effect, and constructs a more generalized component-level reliability evaluation model for related competing failure processes. By constructing a more generalized component-level reliability evaluation model for related competing failure processes, this paper utilizes degradation modeling theory to rationally explain the impact of material self-healing on improving system reliability.

[0133] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0134] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A reliability assessment method for a competing failure system considering the self-healing effect of impact damage, characterized in that: include: Based on degradation modeling theory, the probability that the system will not experience degradation failure is calculated; Based on the cumulative impact damage model, the probability of the system not experiencing degradation failure is used to derive the probability of the system not experiencing impact failure under two conditions: with and without considering the damage self-healing effect. Based on the "degradation-threshold-impact" theory, the reliability function of the system is derived using the probability of the system not experiencing degradation failure and the probability of the system not experiencing impact failure. The reliability function is used to evaluate the reliability of the competing failure system considering the self-healing effect of impact damage. Without considering the damage self-healing effect, the probability of no impact failure of the system is: When the self-healing effect of damage is not considered, the impact damage amount W that causes impact failure is ij1 ,W ij2 ,…does not change with time t and number of shocks N ij (t) changes, cumulative impact damage W i The distribution of (t) is: Assume W ijk Obey the mean The variance is The cumulative impact damage that leads to impact failure is The probability that the system does not experience shock failure is: Among them, D i is the impact failure threshold; m j is the number of external shocks; ij is the intensity function of each impact; The probability of no impact failure of the system considering the damage self-healing effect is: When considering the damage self-healing effect, the impact damage amount W that causes impact failure ij1 ,W ij2 ,…is reduced to W at time t ijk exp[-γ(N ij (t)-k)], cumulative impact damage W i The distribution of (t) is: Assume W ijk Obey the mean The variance is The normal distribution of the impact damage that leads to impact failure is W i (t) also obeys the normal distribution, and its mean is: The variance is: The probability that the system does not experience shock failure is: Where γ is the introduced damage self-healing coefficient, γ>0; D i is the impact failure threshold; m j is the number of external shocks; ij is a function of the intensity of each impact.

2. The reliability assessment method of a competing failure system considering the self-healing effect of impact damage according to claim 1 is characterized in that: The calculation process of the probability that the system does not fail due to degradation is: The Gamma process is introduced to describe the system degradation process: The system starts running at the initial time t = 0 in the best state. The internal degradation amount X(t) obeys the Gamma distribution with shape parameters αt and scale parameters β, respectively. We get X(t) ~ gamma(αt, β), and the probability density function is: Where 1(x≥0) is the indicator function, Γ is the Gamma function, and The distribution function of the internal degradation amount is: where Γ(a,z) is an incomplete Gamma function, and The mean and variance of X(t) are E[X(t)] = αt / β and Var[X(t)] = αt / β respectively. 2 ; Further derive the probability that the system does not experience degradation failure: For a system with correlated competitive failures, the jth affected shock type has a strength of λ ij (t) is a nonhomogeneous Poisson process {N ij (t), t≥0} arrives, the damage amount of the jth effective impact type acting on the system is Y ij1 ,Y ij2 ,…,Y ij1 ,Y ij2 ,…are independent of each other and follow the same distribution, j=1,2,…,|φ i |, the distribution function is: The total performance degradation of the system S i (t) is expressed as: Total performance degradation S i The distribution of (t) is: in, express The n-order Stieltjes convolution of , therefore, the probability that the system does not fail within time t is: Let X i Represents X i (t) is the realization of discretization at time t, denoted by Z i =X i -X i-1 ; Assume that Z1, Z2, ... are independent and identically Gamma distributed random variables with shape parameters α and scale parameters β respectively, and N is X i The discretization of (t) is realized by X i The first time it reaches x, the probability of at least N shocks occurring within time n is: P{N≥n}=P{X i ≤x} Due to X i =Z1+Z2+…+Z i , according to the central limit theorem, we have: The continuous implementation of N is achieved by the Birnbaum-Saunders distribution Expressed as i >>1, Gamma distribution X i Reasonably approximated by the Inverse Gaussian distribution, assuming that Y ijk Obey the mean The variance is The probability that the system does not fail due to degradation is:

3. The reliability assessment method of a competing failure system considering the self-healing effect of impact damage according to claim 1 is characterized in that: The derivation process of the reliability function is: After obtaining the probability that the system will not experience degradation failure and shock failure, the general form of the system reliability function is obtained according to the type of shock affected: Assume that the mth shock type has a strength of λ m The nonhomogeneous Poisson process of arrivals at time t is independent of other shock types, m = 1, 2, ..., M, until the number of arrivals at time t is n m , then the general form of the system reliability function is: Among them, W i (t) is the cumulative impact damage that leads to impact failure.

4. A reliability assessment system for a competitive failure system considering the self-healing effect of impact damage, applying the method according to any one of claims 1 to 3, characterized in that: include: A calculation unit, used to calculate the probability that the system will not fail due to degradation based on degradation modeling theory; A derivation unit is used to derive the probability of the system not failing due to impact under two conditions, one with and the other without considering the damage self-healing effect, based on the cumulative impact damage model and using the probability of the system not failing due to degradation; A reliability function construction unit is used to derive a reliability function of the system based on the "degradation-threshold-impact" theory using the probability of the system not experiencing degradation failure and the probability of the system not experiencing impact failure; the reliability function is used to perform reliability assessment of a competing failure system that considers the self-healing effect of impact damage.

5. An electronic device, characterized in that: The electronic device comprises a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the competitive failure system reliability assessment method considering the self-healing effect of impact damage according to any one of claims 1 to 3.

6. A computer-readable storage medium, characterized in that The device stores a computer program, which, when executed by a processor, implements the reliability assessment method for a competing failure system considering the self-healing effect of impact damage according to any one of claims 1 to 3.

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