High-speed rail sleeper self-healing resource design method and system based on reliability

Abstract

The invention discloses a high-speed rail sleeper self-healing resource design method and system based on reliability, and relates to the technical field of high-speed rail design, and the method comprises the steps: obtaining high-speed rail sleeper data, and depicting a self-healing mechanism and a failure process of a high-speed rail sleeper according to the high-speed rail sleeper data; based on the self-healing mechanism and the failure process, a self-healing resource design decision model is constructed with the goal of minimizing the long-term average cost rate of the high-speed rail sleeper, the self-healing resource input amount and the sleeper replacement age as decision variables and the self-healing resource utilization rate and the sleeper performance index as constraints; and the self-healing resource design decision model is solved through a search algorithm, and the optimal self-healing resource input amount and the optimal sleeper replacement age are obtained. According to the method, the reliability and the cost effectiveness of the sleeper are comprehensively considered, the self-healing resource design optimization model is established, and the method aims at achieving optimal configuration of self-healing resources so as to improve the reliability of the sleeper and reduce the operation and maintenance cost.

Description

Technical Field

[0001] The present invention belongs to the technical field of high-speed rail design, and in particular relates to a reliability-based high-speed rail sleeper self-healing resource design method and system. Background Art

[0002] As a core component of the modern transportation system, the safe and stable operation of high-speed railways is of vital importance to the efficient operation of the entire transportation network. With the increasing demand for high-speed rail transportation, sleepers, a key element of high-speed rail infrastructure, are facing unprecedented severe tests. Sleepers not only need to withstand the increasingly frequent and intense dynamic loads generated by train operation, but also need to resist erosion from the natural environment and possible catastrophic impacts. The continuous maintenance of their performance is crucial to the safe operation of high-speed rail.

[0003] At present, prestressed concrete sleepers are the mainstream choice. In the process of bearing heavy pressure and environmental erosion for a long time, their performance gradually declines, which may lead to premature failure, thus posing a potential threat to the safe operation of high-speed rail. In order to meet this challenge, researchers and industry experts began to explore the application of self-healing concrete technology in sleeper manufacturing. Self-healing concrete is embedded with self-healing resources such as repair agents, which can automatically trigger the repair mechanism after the sleeper is damaged, thereby extending its service life, improving the safety of high-speed rail operation, and significantly reducing subsequent maintenance costs.

[0004] However, the introduction of self-healing concrete technology is not without challenges. On the one hand, the embedding of self-healing resources requires a high initial investment, which has a direct impact on the economic benefits of high-speed rail construction; on the other hand, the amount of self-healing resources configured is directly related to the self-healing efficiency and long-term reliability of the sleepers. Insufficient configuration may result in the sleepers being unable to be effectively repaired after being damaged, thereby threatening the safe operation of the high-speed rail; while excessive configuration will cause a waste of self-healing resources and increase unnecessary cost burdens. Therefore, how to reasonably determine the amount of self-healing resources invested while ensuring the reliability of the sleepers and achieve dual optimization of performance and economic costs has become a technical problem that needs to be solved urgently.

[0005] To address this problem, the present invention proposes a reliability-based high-speed railway sleeper self-healing resource design method and system. Summary of the invention

[0006] In order to solve the shortcomings of the prior art, the present invention proposes a reliability-based high-speed railway sleeper self-healing resource design method and system. By comprehensively considering the reliability and cost-effectiveness of the sleepers, a self-healing resource design optimization model is established, aiming to achieve the optimal configuration of self-healing resources, so as to improve the reliability of the sleepers and reduce the operation and maintenance costs.

[0007] The present invention is achieved through the following technical solutions:

[0008] On the one hand, the present invention provides a reliability-based high-speed railway sleeper self-healing resource design method, the method comprising:

[0009] Acquire high-speed rail sleeper data, and characterize the self-healing mechanism and failure process of the high-speed rail sleeper according to the high-speed rail sleeper data;

[0010] Based on the self-healing mechanism and failure process, with the goal of minimizing the long-term average cost rate of high-speed rail sleepers, the self-healing resource input and sleeper replacement age are used as decision variables, and the self-healing resource utilization rate and sleeper performance indicators are used as constraints to construct a self-healing resource design decision model.

[0011] The self-healing resource design decision model is solved by a search algorithm to obtain the optimal self-healing resource input and the optimal sleeper replacement age.

[0012] Specifically, the high-speed railway sleeper data includes self-healing design principles, degradation failure data and failure thresholds.

[0013] Specifically, the self-healing mechanism and failure process of the sleepers are characterized according to the high-speed railway sleeper data, including: using random processes to mathematically characterize the self-healing mechanism and failure process of the high-speed railway sleepers, including distinguishing the different effects of type I impact and type II impact on the sleepers, wherein type I impact can be self-healed by the self-healing resources embedded in the sleepers, and type II impact cannot be self-healed, and revealing the correlation between them.

[0014] Specifically, the self-healing mechanism and failure process of high-speed rail sleepers are mathematically characterized using random processes, including:

[0015] The sleeper has K + 1 degradation states, corresponding to the cumulative damage caused by type I impact, and the state space is S = {0, 1, 2, …, K}, where 0 represents the perfect state and N represents the failure state;

[0016] There are M units of self-healing resources in the sleeper. Every time interval Z, the sleeper will make a self-healing attempt to transfer the degraded state from i (1≤i<K) to the adjacent degraded state i-1;

[0017] The sleeper has M+1 self-healing resource consumption states, and the state space is H = {0, 1, ..., M}. When the sleeper is in the degraded state i (1≤i<K), each self-healing attempt will be performed with probability η i,mn The self-healing resource consumption state is transferred from m(m∈H) to n(m≤n≤M), and there is

[0018] The occurrence of type I shocks follows a homogeneous Poisson process with parameter λ1, and each shock occurs with a certain probability γ i,j The sleeper is transferred from degraded state i to degraded state j, and there is

[0019] The occurrence of type II impact follows a homogeneous Poisson process with parameter λ2, and the damage caused by each type II impact to the sleeper depends on the current degradation state of the sleeper. When the sleeper is in degradation state i, the damage caused by the g-th type II impact to the system is Y i,g , are independent and identically distributed random variables, whose cumulative distribution function and probability density function are and When the damage caused by a certain type II impact exceeds the failure threshold D that the sleeper can withstand, the sleeper fails.

[0020] Specifically, the self-healing resource design decision model is:

[0021]

[0022] Among them, M and τ represent the input of self-healing resources and the age of sleeper replacement, respectively. p represents the purchase cost of new sleepers, C m M represents the cost of self-healing resources, C o E(T o ) represents the cost of sleeper operation, C f represents the cost of sleeper failure, represents the maintenance cost of replacing the sleeper, E(T o ), E(M) represent the average operating time and average replacement time of the sleeper in a replacement cycle, R(τ) represents the reliability of the sleeper at time τ, and r u (E(T o )) represents the average self-healing resource utilization rate of the sleeper in one update cycle, U min represents the average self-healing resource utilization threshold, A represents the steady-state availability of the sleeper, and A min Indicates the steady-state availability threshold.

[0023] Specifically, solving the self-healing resource design decision model through a search algorithm includes:

[0024] Set the thresholds of self-healing resource utilization and steady-state availability, as well as the number of iterations; initialize the minimum long-term operating cost rate and the corresponding optimal self-healing resource input and optimal sleeper replacement age;

[0025] If the steady-state availability of the sleeper is not less than the threshold A min , then calculate the average self-healing resource utilization of the sleeper;

[0026] If the average self-healing resource utilization of the sleeper is not less than the threshold U min , then calculate the long-term average cost rate;

[0027] If the long-term average operating cost rate does not change after multiple consecutive iterations in the inner loop, the inner loop is stopped and the outer loop is performed;

[0028] If the long-term average operating cost rate does not change after multiple consecutive iterations in the outer loop, the outer loop is stopped and it is considered that the optimal solution has been approached or reached.

[0029] On the other hand, the present invention provides a reliability-based high-speed railway sleeper self-healing resource design system, the system comprising:

[0030] An initialization module, used to obtain high-speed rail sleeper data, and characterize the self-healing mechanism and failure process of the high-speed rail sleeper according to the high-speed rail sleeper data;

[0031] A model building module is used to build a self-healing resource design decision model based on the self-healing mechanism and failure process, with the goal of minimizing the long-term operation cost rate of high-speed rail sleepers, with the self-healing resource input and the sleeper replacement age as decision variables, and with the self-healing resource utilization rate and sleeper performance indicators as constraints;

[0032] The model solving module is used to solve the self-healing resource design decision model through a search algorithm to obtain the optimal self-healing resource input and the optimal sleeper replacement age.

[0033] The beneficial effects of the present invention are:

[0034] The present invention fully considers the dual effects of performance improvement and cost increase brought about by embedding self-healing resources in high-speed rail sleepers, and constructs an optimization model for self-healing resource design. Under the dual constraints of self-healing resource utilization rate and sleeper reliability index, the model achieves dual optimization of self-healing resource investment and sleeper replacement timing by minimizing the long-term operating cost rate of sleepers. While ensuring the high reliability of high-speed rail sleepers, the present invention achieves effective control of operation and maintenance costs, achieving a perfect balance between the two. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 A flow chart of the method described in the present invention;

[0036] Figure 2 A sample path diagram of possible performance degradation of high-speed railway sleepers;

[0037] Figure 3 The trend of the long-term average operating cost rate of high-speed railway sleepers;

[0038] Figure 4 The changing trend of high-speed railway sleeper self-healing resource utilization rate;

[0039] Figure 5 is the trend of steady-state availability of high-speed railway sleepers;

[0040] Figure 6 This is a structural diagram of the system described in the patent of this invention. DETAILED DESCRIPTION

[0041] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. 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 creative work should fall within the scope of protection of the present invention.

[0042] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0043] Example 1

[0044] like Figure 1 As shown, an embodiment of the present invention provides a reliability-based high-speed railway sleeper self-healing resource design method, the method comprising:

[0045] Step 1, obtaining high-speed rail sleeper data; and characterizing the self-healing mechanism and failure process of the high-speed rail sleeper based on the high-speed rail sleeper data.

[0046] Specifically, the high-speed railway sleeper data includes self-healing design principles, degradation failure data and failure thresholds.

[0047] The high-speed railway sleepers involved in the embodiments of the present invention are embedded with self-healing resources, and can randomly respond to two types of impacts during operation: Type I impact and Type II impact. Among them, the damage caused by Type I impact can be spontaneously repaired by the sleepers consuming self-healing resources; while Type II impact will cause direct and irreversible damage to the system. The self-healing ability of high-speed railway sleepers depends on the consumption of self-healing resources. Once the self-healing resources are exhausted, the sleepers will lose their self-healing ability. Both types of impacts may cause the sleepers to fail, thus constituting a competitive failure process.

[0048] Based on the above content, in this embodiment, the self-healing mechanism and failure process of the sleepers are characterized according to the high-speed rail sleeper data, including: using random processes to mathematically characterize the self-healing mechanism and failure process of the high-speed rail sleepers, including distinguishing the different effects of type I impact and type II impact on the sleepers, where type I impact can be self-healed by the self-healing resources embedded in the sleepers, and type II impact cannot be self-healed, and revealing the correlation between them.

[0049] Furthermore, the self-healing mechanism and failure process of high-speed rail sleepers are mathematically characterized using random processes, including:

[0050] Self-healing resources and type I impact characterization

[0051] (1) There are K+1 degradation states of high-speed rail sleepers, corresponding to the cumulative damage caused by type I impact. The state space is denoted as S = {0, 1, 2, ..., K}, and the increase in numbers indicates the degradation of sleeper performance. 0 and K are the perfect state and failure state, respectively, so the working state set of the sleeper is defined as S W = {0, 1, 2, ..., K-1}. Let S(t) = i to indicate that the sleeper is in damage state i at time t.

[0052] (2) The occurrence of type I shocks follows a homogeneous Poisson process with parameter λ1 {N1(t), t≥0}, where N1(t) represents the number of type I shocks that occur within the time (0, t]. Each type I shock will cause damage to the high-speed rail sleeper with a certain probability, causing the sleeper to transfer to a higher degradation state. Specifically, when the sleeper is in the degradation state i(i∈S W ), the probability that the sleeper is transferred to the degraded state j due to the subsequent type I impact is γ i,j , and there are

[0053] (3) The high-speed rail sleeper has M units of self-healing resources embedded in it. The consumption of self-healing resources enables the sleeper to spontaneously repair the damage caused by type I impact. Define a random variable Z, whose cumulative distribution function is F Z (t) = 1-e -βt . Every time interval Z, the sleeper will make a self-healing attempt to transfer the current degraded state to the adjacent, better state, that is, from i (1≤i<K) to i-1. The success of each self-healing attempt depends on two key conditions: first, no type I shock occurs during the time interval Z, or even if a type I shock occurs, the degraded state of the system is not changed; second, the successful release of self-healing resources, which will be explained in assumption (4).

[0054] (4) Corresponding to the amount of self-healing resources embedded initially, the high-speed rail sleeper has M+1 self-healing resource consumption states, and the state space is H = {0, 1, ..., M}. When the sleeper is in the degraded state i (1≤i<K), each self-healing attempt will be with probability η i,mn To make the resource consumption state change from m(m∈H) to n(m≤n≤M), we have Note that i,mm It means that the self-healing resources cannot be effectively released due to some factors (such as the sleeper performance level is too low), resulting in the failure of the self-healing attempt. When the sleeper enters the consumption state M, it means that the self-healing resources have been exhausted and the sleeper no longer has the self-healing ability. The definition H(t) = m means that the sleeper is in the consumption state m at time t.

[0055] Type II shock hypothesis

[0056] (1) The occurrence of type II shocks follows a homogeneous Poisson process with parameter λ2 {N2(t), t≥0}, where N2(t) represents the number of type II shocks that occur within the time (0, t). The damage caused by each type II shock to the high-speed rail sleeper depends on the current degradation state of the sleeper. When the sleeper is in degradation state i, the damage caused by the g-th type II shock to the system is Y i,g . are independent and identically distributed random variables, whose cumulative distribution function and probability density function are F Yi (y) and f Yi (y).

[0057] (2) The damage caused by a Type II impact cannot be repaired spontaneously by the sleeper. When the damage caused by a Type II impact exceeds the threshold D that the sleeper can withstand, the system fails.

[0058] It should be noted that the embodiment of the present invention sets a clear replacement criterion for the age replacement strategy of high-speed rail sleepers: once the operation time of the sleeper reaches a preset threshold, or the sleeper fails during operation, it should be replaced immediately. Of these two conditions, the one that occurs first shall prevail. Such a strategy is intended to ensure the safety and reliability of high-speed rail sleepers and avoid safety accidents caused by aging or failure of sleepers.

[0059] In order to better understand the failure process of the high-speed railway sleeper, Figure 2 Two possible sample paths of high-speed railway sleepers are given. Figure 2 As shown in Figure 1, the transition of the degradation state of the high-speed rail sleeper occurs under the combined action of type I impact and the internal self-healing mechanism. Each completion of the self-healing action will randomly consume a certain amount of self-healing resources, so when the self-healing resources are exhausted, the sleeper can no longer self-heal. At the same time, when the high-speed rail sleeper enters the degradation state 5 or when the damage caused by a type II impact is greater than the failure threshold, the sleeper fails.

[0060] Step 2, based on the self-healing mechanism and failure process, with the goal of minimizing the long-term average cost rate of high-speed railway sleepers, with the self-healing resource input and the sleeper replacement age as decision variables, and with the self-healing resource utilization rate and sleeper performance indicators as constraints, a self-healing resource design decision model is constructed.

[0061] The embodiment of the present invention defines the initial self-healing resource input of the high-speed railway sleeper, which is a key parameter. A larger self-healing resource input may significantly improve the performance of the sleeper and enhance its ability to resist impact, but correspondingly, it will also bring higher self-healing resource costs. On the contrary, although a smaller self-healing resource input can save costs, it may sacrifice the performance of the sleeper and increase the risk of failure after impact.

[0062] In order to balance the performance, cost and replacement frequency of sleepers, the present invention proposes the need to optimize the two parameters of self-healing resource input and sleeper replacement age. By comprehensively considering the safety benefits brought by performance improvement, the cost of self-healing resources and the maintenance cost of replacing sleepers, an optimal solution can be found so that the sleepers can not only play the best performance but also control the cost within a reasonable range under the premise of ensuring safety.

[0063] Specifically, the patent of the present invention will aim to minimize the long-term operating cost rate of high-speed railway sleepers, and under the constraints of resource utilization rate and sleeper performance indicators, determine the optimal self-healing resource input M and sleeper replacement age τ.

[0064] After each replacement, the high-speed rail sleepers will be put into operation in a brand new and intact state. Therefore, the end time of each replacement can be regarded as a series of update points. According to the renewal reward theory, the average long-term operating cost rate of the sleepers can be expressed as

[0065]

[0066] E(C) represents the average total cost incurred in a renewal cycle, and E(D) represents the average duration of a renewal cycle. E(D) is calculated from the average sleeper operation time E(T o ) and the average replacement time E(M), that is,

[0067]

[0068] Let the random variable represents the time required for each replacement, and its cumulative distribution function is M(t), then it is easy to know In addition, let the random variable T represent the life of the sleeper, and its cumulative distribution function, probability density function and reliability function are distributed as F(t), f(t) and R(t). Under the age replacement strategy, the average operating time of the sleeper in one renewal cycle is

[0069]

[0070] The Laplace transform of equation (3) with respect to τ is:

[0071]

[0072] Therefore, E(T o ) can be done by -1 R * (s) is obtained by performing inverse Laplace transform on s.

[0073] In one renewal cycle, the total cost of high-speed rail sleepers includes the following five parts:

[0074] The purchase cost of new sleepers C p , which does not include the investment cost of self-healing resources;

[0075] Self-healing resource investment cost C m M, where C m Represents the cost of self-healing resources per unit;

[0076] Cost of sleeper operation C o E(T o ), where C o It represents the cost generated per unit of high-speed rail sleeper operation time;

[0077] Cost of sleeper failure C f , which includes economic losses and safety losses caused by sleeper failure;

[0078] Maintenance costs for replacing sleepers Among them C r Represents the cost incurred per unit of maintenance time.

[0079] Based on this, the average total cost incurred in an update cycle is

[0080]

[0081] Substituting equations (2) to (4) into equation (1), we can get the calculation formula for the long-term operation cost rate, which is the objective function of the joint optimization model. In order to ensure the effective use of resources and the stable operation of the system, two constraints are added to the model. First, the average self-healing resource utilization rate cannot be lower than the given minimum value U min Let r u (t) represents the self-healing resource utilization rate at time t, then the constraint can be expressed as r u (E(T o ))≥U minSecond, the steady-state availability A of the sleeper must be greater than the set threshold A min The steady-state availability can be calculated by dividing the average operating time of the sleeper in one update cycle by the average duration of one update cycle, that is,

[0082]

[0083] Considering the real-world scenario, assume that M and τ are non-zero positive integers. Therefore, based on the above analysis, the self-healing resource design decision model is:

[0084]

[0085] Among them, M and τ represent the input of self-healing resources and the age of sleeper replacement, respectively. p The purchase cost of new sleepers, C m M represents the cost of self-healing resources, C o E(T o ) represents the cost of sleeper operation, C f represents the cost of sleeper failure, represents the maintenance cost of replacing the sleeper, E(T o ), E(M) represent the average operating time and average replacement time of the sleeper in a replacement cycle, R(τ) represents the reliability of the sleeper at time τ, and r u (E(T o )) represents the average self-healing resource utilization rate of the sleeper in one update cycle, U min represents the average self-healing resource utilization threshold, A represents the steady-state availability of the sleeper, and A min Indicates the steady-state availability threshold.

[0086] In the process of constructing the self-healing resource design decision model, it is also necessary to calculate the reliability R(t) of high-speed rail sleepers and the utilization rate of self-healing resources r u (t).

[0087] Specifically, the calculation process of high-speed railway sleeper reliability R(t) includes:

[0088] The reliability of the high-speed rail sleeper at time t means that the sleeper does not enter the failure degradation state K in the time interval (0, t], and the damage caused by all the type II impacts is less than the threshold D. Its mathematical expression is:

[0089] R(t)=P{S(t)<K,Y(t)<D},Y(t) represents the maximum value of damage caused by type II impact at time t.

[0090] When the sleeper is in the degraded state at time 0, i(i∈S W ), when the resource consumption state is m(m∈H), its conditional reliability function at time t is

[0091]

[0092] in, represents the ath time when the sleeper degradation state changes, S a and H a This means that the sleeper is at C a The degradation state and resource consumption state at the moment. In addition, let C0 = 0, which indicates the starting point of the sleeper operation. Therefore, the evolution of the sleeper degradation state can be modeled as a homogeneous Markov update process The corresponding semi-Markov kernel is defined as V(t) = {V mn,ij (t); m,n∈H; i,j∈S}.

[0093] V mn,ij (t)={H1=n, S1=j, C1≤t|H0=m, S0=i}.

[0094] Get R m,i The analytical expression of (t) is the premise for deriving R(t). At the same time, according to formula (7), when solving R m,i (t) process inevitably requires the determination of V mn,ij (t). Therefore, firstly, Lemma 1 gives V mn,ij The calculation formula of (t).

[0095] Lemma 1: V mn,ij The Laplace transform of (t) with respect to t is

[0096]

[0097] Proof: According to the evolution law of system degradation state and resource consumption state, we can first get the following important conclusions:

[0098] For any i, j∈S, when n<m, V mn,ij (t) = 0. Because without external resource replenishment, as the self-healing resource consumption increases, the consumption state can only shift to a higher level.

[0099] For any m∈H, when j<i, V mm,ij (t) = 0. j < i indicates that a self-healing action is successfully completed, so the resource consumption state cannot remain unchanged.

[0100] For any m, n∈H, when 2≤i≤K-1 and j=i-2,i-3,…,0, V mn,ij (t) = 0. This is because the assumption limits each self-healing action to only one unit of improvement from the degraded state of the system.

[0101] Based on the above important conclusions, V mn,ij The derivation of (t) needs to consider the following four situations.

[0102] Case 1: S0 = i (0 ≤ i < K), H0 = M; S1 = j (i < j ≤ K), H1 = M.

[0103] In this case, the initial self-healing resource state of the sleeper is M, indicating that the embedded self-healing resources have been consumed and no longer have self-healing ability. Therefore, the change in the degradation state of the sleeper can only be caused by a specific type I impact. Based on this,

[0104]

[0105] Among them, N c Represents the number of I-type shocks that occur until the first degradation state changes. Φ a represents the time when the a-th type I shock occurs. Because the arrival of type I shocks follows a homogeneous Poisson process, Φ a is a gamma-distributed random variable with shape parameter a and scale parameter λ1, and its PDF is

[0106]

[0107] CDF for Q a (t) = P{Φ a ≤t}.

[0108] Case 2: S0=0, H0=m(0≤m≤M); S1=j(0<j≤K), H1=m,

[0109] In this case, the sleeper's initial degradation state is 0, so its first transfer can only be to a higher degradation state. Similar to case 1, there is

[0110]

[0111] Case 3: S0 = i (1 ≤ i < K), H0 = m (0 ≤ m < M); S1 = i-1, H1 = n (m < n ≤ M)

[0112] In this case, the sleeper successfully completed 1 self-healing action, consuming (nm) units of self-healing resources. According to the assumption, the sleeper will make a self-healing attempt every time interval Z. Therefore, before time t, at least 1 self-healing attempt has occurred. Let Υ b represents the time when the bth self-healing attempt occurs. Since Z follows an exponential distribution with parameter β, Υ b It follows a gamma distribution with shape parameter b and scale parameter β.

[0113] Its cumulative distribution function is the probability density function, denoted by G b (t) and g b (t).

[0114]

[0115] Case 4: S0 = i (1 ≤ i < K), H0 = m (0 ≤ m < M); S1 = j (i < j ≤ K), H1 = m.

[0116] In this case, the sleeper failed to complete a self-healing action. The change in its degradation state was due to a type I impact.

[0117]

[0118] The first term on the right: Z>Φ a This means that before the first self-healing attempt occurs, the sleeper has already moved to a higher degradation state due to the Type I impact, so there is

[0119]

[0120] The second term on the right side: Z≤Φ a Indicates that there was at least one self-healing attempt before the sleeper degradation state changed, but because the self-healing resources were not successfully released, all self-healing attempts failed.

[0121]

[0122] Combining the above two items, we can get

[0123]

[0124] By performing Laplace transform on equations (8) to (11) with respect to t, we can obtain Lemma 1.

[0125] Based on Lemma 1, Theorem 1 gives the conditional reliability R m,i (t) The expression after Laplace transformation. Theorem 1: Conditional reliability R m,i The Laplace transform of (t) with respect to the time parameter t is

[0126]

[0127] in,

[0128] Proof: The two terms on the right side of equation (7) are discussed below.

[0129] The first item on the right side: The event {C1>t} indicates that the degradation state of the sleeper has not changed within (0, t], so there is

[0130]

[0131] Among them, P{Y(t)<D|C1>t,S0=i,H0=m} represents the probability that the maximum value of type II impact damage suffered by the sleeper in (0,t] is less than the threshold D under the condition that the initial resource consumption state is m, the degradation state is i and remains unchanged until time t. Its expression is

[0132]

[0133] The second term on the right side: When C1≤t, we have

[0134]

[0135] In summary, we can get

[0136]

[0137] Theorem 1 can be obtained by performing Laplace transform with respect to t.

[0138] Define the following matrix:

[0139]

[0140] Then equation (12) can be written in matrix form

[0141] R * (s) = Θ * (s)-Γ * (s)1 (M+1)×(K+1) +Φ * (s)Ω * (s)R * (s),

[0142] Arrangement available

[0143] R * (s)=(I-Φ * (s)Ω * (s))(Θ * (s)-Γ * (s)1 (M+1)×(K+1) ). (13)

[0144] Among them, 1 (M+1)×(K+1) Represents an (M+1)(K+1)-dimensional column vector whose elements are all 1.

[0145] Let ζ=(ζ0,ζ1,…,ζ M) represents the distribution vector of the initial consumption state of the self-healing resource. Because the degradation state K is a failure state, once the high-speed rail sleeper enters this state, it will not be able to recover to other states without external maintenance intervention. Therefore, in the reliability solution, the initial distribution of the sleeper degradation state is expressed as α=(α0,α1,…,α K-1 ). According to formula (13), the reliability of the sleeper at time t is

[0146] R * (s)=θR * (s), (14)

[0147] Among them, θ=(ζ0α,ζ1α,…,ζ M α). The reliability of the sleeper at time t can be obtained by performing an inverse Laplace transform on equation (14) with respect to s.

[0148] Specifically, the self-healing resource utilization rate r u (t) The specific calculation process is:

[0149] Self-healing resource utilization rate r at time t u (t) is defined as the ratio of the consumed self-healing resources to the initial self-healing resources of the high-speed rail sleeper, and its mathematical expression is:

[0150]

[0151] E[H(t)] represents the average amount of self-healing resources consumed by the sleeper at time t.

[0152]

[0153] To solve the value of P{H(t)=n}, define a new conditional probability W mn,ij (t), which is expressed as

[0154] W mn,ij (t)=P{H(t)=n, S(t)=j|S0=i, H0=m}, i, j∈S; m, n∈E.

[0155] W mn,ij (t) represents the probability that the degradation state is j and the resource consumption state is n at time t, given that the initial degradation state of the high-speed rail sleeper is i and the resource consumption state is m. Theorem 2 gives W mn,ij (t) Expression after Laplace transformation.

[0156] Theorem 2: W mn,ij The Laplace transform of (t) with respect to t is

[0157]

[0158] Proof: It is easy to see that for any i, j∈S, when n<m, W mn,ij (t) = 0; at the same time, when j < i, W mm,ij (t) = 0. In addition, W mn,ij The derivation of (t) needs to consider the following four situations.

[0159] Case 1: S0=i(0≤i<K),H0=m(0≤m≤M);S(t)=i,H(t)=m.

[0160] Based on whether the first degradation state change time C1 is earlier than time t, W mm,ij (t) can be further written

[0161] W mm,ii (t)=P{H(t)=m,S(t)=i|S0=i,H0=m}

[0162] =P{H(t)=m, S(t)=i, C1>t|S0=i, H0=m}

[0163] +P{H(t)=m, S(t)=i, C1≤t|S0=i, H0=m}.

[0164] The first term on the right: C1>t indicates that the first degradation state change is later than time t, so at time t the system is still in the initial degradation state and resource consumption state,

[0165]

[0166] The second term on the right: C1≤t indicates that the first degradation state change occurs earlier than time t. To ensure that the system is still in the initial degradation state and resource consumption state at time t, the sleeper must fail due to type II impact before time C1, that is, Y(C1)>D.

[0167]

[0168] Therefore, we can get

[0169]

[0170] Case 2: S0=i(0≤i<K), H0=m(0≤m<M); S(t)=i, H(t)=n(m<n≤M).

[0171] In case 2, the resource consumption state has changed, which means that the degradation state must have changed before time t, so C1≤t. Based on this,

[0172]

[0173] Case 3: S0=i(0≤i<K),H0=m(0≤m<M);S(t)=K,H(t)=n(m≤n≤M).

[0174] S(t)=K indicates that the sleeper has entered a degraded state before time t and has failed. After this failure, the system degradation state and resource consumption state no longer change.

[0175]

[0176] Among them, P{H(t)=n,S(t)=K|S1=K,H1=n,C1=x}=1, and for e≠n,

[0177] P{H(t)=n, S(t)=K|S1=K, H1=e, C1=x}=0.

[0178] Scenario 4:

[0179] S0=i(0≤i<K), H0=m(0≤m≤M); S(t)=j(0≤j<K, j≠i), H(t)=n(m≤n≤M).

[0180]

[0181] Theorem 2 can be obtained by performing Laplace transformation on equations (16) to (19) with respect to t. To solve W mn,ij (t), define the following matrix:

[0182] in in

[0183]

[0184] in

[0185]

[0186] The equation in Theorem 2 can be written in matrix form

[0187]

[0188] Reorganize into

[0189]

[0190] The value of W(t) can be obtained by performing Laplace inversion on equation (20).

[0191] According to formula (20), we can get

[0192]

[0193] Among them, ρ n is a (K+1)(M+1)-dimensional column vector, whose n(K+1)+1, n(K+1)+2, ..., (n+1)(K+1)th elements are 1, and the rest are 0. Substituting the calculated value of P{H(t)=n} into formula (15), the average utilization rate of self-healing resources at time t can be obtained.

[0194] Step 3, solving the self-healing resource design decision model through a search algorithm to obtain the optimal self-healing resource input and the optimal sleeper replacement age.

[0195] In the embodiment of the present invention, the self-healing resource design decision model is solved by a search algorithm, including: setting thresholds of self-healing resource utilization and steady-state availability, and the number of iterations; initializing the minimum long-term operating cost rate and the corresponding optimal self-healing resource investment and optimal sleeper replacement age; if the steady-state availability of the sleeper is not less than the threshold A min , then calculate the average self-healing resource utilization of the sleeper; if the average self-healing resource utilization of the sleeper is not less than the threshold U min , then calculate the long-term average cost rate; if the long-term average operating cost rate does not change after multiple consecutive iterations in the inner loop, stop the inner loop and proceed to the outer loop; if the long-term average operating cost rate does not change after multiple consecutive iterations in the outer loop, stop the outer loop and consider that the optimal solution has been approached or reached.

[0196] Specifically, the detailed implementation process of the search algorithm is shown in Table 1 below.

[0197] Table 1

[0198]

[0199]

[0200] In order to better understand the technical solution of the present invention, a specific high-speed railway sleeper is taken as an example for detailed description below.

[0201] Consider a high-speed railway sleeper put into use at time 0. During its operation, it will be randomly affected by two types of shocks: Type I shock and Type II shock.

[0202] The occurrence of type I impact obeys a homogeneous Poisson process with parameter λ1 = 0.5. Corresponding to the cumulative damage caused by type I impact, the high-speed rail sleeper has 6 degradation states, denoted as S = {0, 1, 2, 3, 4, 5}, and the corresponding working state set is S W ={0,1,2,3,4}. For any degenerate state i∈S W, as shown in Table 2, which gives the state transition probability caused by type I impact. For example, when the sleeper is in degradation state 1, there is a certain probability that it will transfer to other degradation states or remain in the original state due to type I impact. When the sleeper enters degradation state 5, it is considered to have failed.

[0203] The occurrence of type II impact also obeys the homogeneous Poisson distribution, but its parameter is λ2 = 0.1. The damage caused by each type II impact to the sleeper depends on the current degradation state of the sleeper. Under different degradation states, it is assumed that the damage caused by type II impact obeys a normal distribution with different means and variances, that is, Y0~TN{1.2,0.2,0,∞}, Y1~TN{1.2,0.25,0,∞}, Y2~TN{1.25,0.21,0,∞}, Y3~TN{1.27,0.21,0,∞}, Y4~TN{1.3,0.24,0,∞}. At the same time, when the damage caused by a type II impact exceeds the threshold D = 1.5, the sleeper fails.

[0204] Table 2 γ ij (i∈S W ,j∈S,i≤j)

[0205]

[0206]

[0207] Assume the cost parameter is C p =4, C f =20, C m =0.5, C o =0.2, C r =0.1. Based on this, the long-term average operating cost rate of the sleeper changes with the change trend of the self-healing resource input M and the replacement age τ as follows: Figure 3 At the same time, according to equations (15) and (5), the changing trends of sleeper self-healing resource utilization and steady-state availability can be calculated, as follows: Figure 4 and Figure 5 shown.

[0208] In the self-healing resource design decision model, it is required that the average self-healing resource utilization rate cannot be less than the threshold U min =0.65, the steady-state availability of the sleeper cannot be less than A min =0.8. According to the optimization algorithm in Table 1, the number of iterations is set to IterationNum=50, and the minimum long-term operating cost rate can be obtained as ω * =1.85692, corresponding to the optimal self-healing resource input of M * =4, the sleeper replacement age is τ * =12.

[0209] Example 2

[0210] like Figure 6 As shown, an embodiment of the present invention provides a reliability-based high-speed railway sleeper self-healing resource design system, the system comprising:

[0211] An initialization module, used to obtain high-speed rail sleeper data, and characterize the self-healing mechanism and failure process of the high-speed rail sleeper according to the high-speed rail sleeper data;

[0212] A model building module is used to build a self-healing resource design decision model based on the self-healing mechanism and failure process, with the goal of minimizing the long-term operation cost rate of high-speed rail sleepers, with the self-healing resource input and the sleeper replacement age as decision variables, and with the self-healing resource utilization rate and sleeper performance indicators as constraints;

[0213] The model solving module is used to solve the self-healing resource design decision model through a search algorithm to obtain the optimal self-healing resource input and the optimal sleeper replacement age.

[0214] It should be understood that the reliability-based high-speed rail sleeper self-healing resource design system provided in the embodiment of the present invention and the reliability-based high-speed rail sleeper self-healing resource design system provided in the above embodiment are based on the same inventive concept. For more specific working principles of each module in the embodiment of the present invention, please refer to the above embodiment and will not be repeated in this embodiment.

Claims

1. A reliability-based high-speed railway sleeper self-healing resource design method, characterized in that: include: Acquire high-speed rail sleeper data, and characterize the self-healing mechanism and failure process of the high-speed rail sleeper according to the high-speed rail sleeper data; Based on the self-healing mechanism and failure process, with the goal of minimizing the long-term average cost rate of high-speed rail sleepers, the self-healing resource input and sleeper replacement age are used as decision variables, and the self-healing resource utilization rate and sleeper performance indicators are used as constraints to construct a self-healing resource design decision model. The self-healing resource design decision model is solved by a search algorithm to obtain the optimal self-healing resource input and the optimal sleeper replacement age.

2. A reliability-based high-speed railway sleeper self-healing resource design method according to claim 1, characterized in that: The high-speed railway sleeper data includes self-healing design principles, degradation failure data and failure thresholds.

3. According to a reliability-based high-speed railway sleeper self-healing resource design method according to claim 1, it is characterized in that: The self-healing mechanism and failure process of the sleepers are characterized according to the high-speed railway sleeper data, including: using random processes to mathematically characterize the self-healing mechanism and failure process of the high-speed railway sleepers, including distinguishing the different effects of type I impact and type II impact on the sleepers, wherein type I impact can be self-healed by the self-healing resources embedded in the sleepers, and type II impact cannot be self-healed, and revealing the correlation between them.

4. A reliability-based high-speed railway sleeper self-healing resource design method according to claim 3, characterized in that: The self-healing mechanism and failure process of high-speed rail sleepers are mathematically characterized using random processes, including: The sleeper has K + 1 degradation states, corresponding to the cumulative damage caused by type I impact, and the state space is S = {0, 1, 2, …, K}, where 0 represents the perfect state and N represents the failure state; There are M units of self-healing resources in the sleeper. Every time interval Z, the sleeper will make a self-healing attempt to transfer the degraded state from i (1≤i<K) to the adjacent degraded state i-1; The sleeper has M+1 self-healing resource consumption states, and the state space is H = {0, 1, ..., M}. When the sleeper is in the degraded state i (1 ≤ i < K), each self-healing attempt will be performed with probability η i,mn The self-healing resource consumption state is transferred from m(m∈H) to n(m≤n≤M), and there is The occurrence of type I shocks follows a homogeneous Poisson process with parameter λ1, and each shock occurs with a certain probability γ i,j The sleeper is transferred from degraded state i to degraded state j, and there is The occurrence of type II impact follows a homogeneous Poisson process with parameter λ2, and the damage caused by each type II impact to the sleeper depends on the current degradation state of the sleeper. When the sleeper is in degradation state i, the damage caused by the g-th type II impact to the system is Y i,g , are independent and identically distributed random variables, whose cumulative distribution function and probability density function are and When the damage caused by a type II impact exceeds the failure threshold D that the sleeper can withstand, the sleeper fails.

5. The reliability-based high-speed railway sleeper self-healing resource design method according to claim 1 is characterized in that: The self-healing resource design decision model is: Among them, M and τ represent the input of self-healing resources and the age of sleeper replacement, respectively. p represents the purchase cost of new sleepers, C m M represents the cost of self-healing resources, C o E(T o ) represents the cost of sleeper operation, C f represents the cost of sleeper failure, represents the maintenance cost of replacing the sleeper, E(T o ), E(M) represent the average operating time and average replacement time of the sleeper in a replacement cycle, R(τ) represents the reliability of the sleeper at time τ, and r u (E(T o )) represents the average self-healing resource utilization rate of the sleeper in one update cycle, U min represents the average self-healing resource utilization threshold, A represents the steady-state availability of the sleeper, and A min Indicates the steady-state availability threshold.

6. The reliability-based high-speed railway sleeper self-healing resource design method according to claim 1 is characterized in that: Solving the self-healing resource design decision model through a search algorithm includes: Set the thresholds of self-healing resource utilization and steady-state availability, as well as the number of iterations; initialize the minimum long-term operating cost rate and the corresponding optimal self-healing resource input and optimal sleeper replacement age; If the steady-state availability of the sleeper is not less than the threshold A min , then calculate the average self-healing resource utilization of the sleeper; If the average self-healing resource utilization of the sleeper is not less than the threshold U min , then calculate the long-term average cost rate; If the long-term average operating cost rate does not change after multiple consecutive iterations in the inner loop, the inner loop is stopped and the outer loop is performed; If the long-term average operating cost rate does not change after multiple consecutive iterations in the outer loop, the outer loop is stopped and it is considered that the optimal solution has been approached or reached.

7. A reliability-based high-speed railway sleeper self-healing resource design system, characterized in that: include: An initialization module, used to obtain high-speed rail sleeper data, and characterize the self-healing mechanism and failure process of the high-speed rail sleeper according to the high-speed rail sleeper data; A model building module is used to build a self-healing resource design decision model based on the self-healing mechanism and failure process, with the goal of minimizing the long-term operation cost rate of high-speed rail sleepers, with the self-healing resource input and the sleeper replacement age as decision variables, and with the self-healing resource utilization rate and sleeper performance indicators as constraints; The model solving module is used to solve the self-healing resource design decision model through a search algorithm to obtain the optimal self-healing resource input and the optimal sleeper replacement age.

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