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

Abstract

The application discloses a high-speed rail sleeper self-recovery resource design method and system based on reliability, relates to the technical field of high-speed rail design, and comprises the following steps: obtaining high-speed rail sleeper data, and describing the self-recovery mechanism and failure process of the high-speed rail sleeper according to the high-speed rail sleeper data; based on the self-recovery mechanism and the failure process, taking the minimization of the long-term average cost rate of the high-speed rail sleeper as a target, taking the self-recovery resource input and the sleeper replacement age as decision variables, and taking the self-recovery resource utilization rate and the sleeper performance index as constraints, a self-recovery resource design decision model is constructed; and the self-recovery resource design decision model is solved through a search algorithm to obtain the optimal self-recovery resource input and the optimal sleeper replacement age. According to the application, the reliability and cost benefit of the sleeper are comprehensively considered, a self-recovery resource design optimization model is established, and the optimal configuration of the self-recovery resource is realized, so that the reliability of the sleeper is improved and the operation and maintenance cost is reduced.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of high-speed rail design, and particularly relates to a high-speed rail sleeper self-healing resource design method and system based on reliability. BACKGROUND

[0002] As a core component of modern transportation systems, the safe and stable operation of high-speed rail is of great significance to the efficient operation of the entire transportation network. With the continuous rise in demand for high-speed rail transportation, the sleeper, a key element of high-speed rail infrastructure, is facing unprecedented challenges. Sleepers not only need to withstand the increasingly frequent and intense dynamic loads generated by train operation, but also need to resist the erosion of the natural environment and possible catastrophic impacts. The continuous maintenance of its performance is crucial to the safe operation of high-speed rail.

[0003] Currently, as the mainstream choice, prestressed concrete sleepers gradually decline in performance during long-term pressure and environmental erosion, which may lead to premature failure and thus pose a potential threat to the safe operation of high-speed rail. To address this challenge, researchers and industry experts have begun to explore the application of self-healing concrete technology in sleeper manufacturing. Self-healing concrete has embedded self-healing resources such as repair agents, which can automatically trigger a 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 directly affects the economic benefits of high-speed rail construction. On the other hand, the amount of self-healing resources directly affects the self-healing efficiency and long-term reliability of sleepers. Insufficient allocation may result in ineffective repair of sleepers after damage, thereby threatening the safe operation of high-speed rail; while excessive allocation will result in waste of self-healing resources, increasing unnecessary cost burden. Therefore, how to reasonably determine the amount of self-healing resources while ensuring the reliability of sleepers, achieving the dual optimization of performance and economic cost, has become a technical problem that needs to be solved.

[0005] To solve this problem, the present application proposes a high-speed rail sleeper self-healing resource design method and system based on reliability. SUMMARY

[0006] To solve the shortcomings of the prior art, the present application proposes a high-speed rail sleeper self-healing resource design method and system based on reliability. By comprehensively considering the reliability and cost-effectiveness of sleepers, a self-healing resource design optimization model is established to achieve the optimal allocation of self-healing resources, thereby improving the reliability of sleepers and reducing operation and maintenance costs.

[0007] The present application is realized by the following technical solutions:

[0008] In one aspect, the application provides a high-speed rail sleeper self-healing resource design method based on reliability, which comprises:

[0009] Obtaining high-speed rail sleeper data, and describing 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, a self-healing resource design decision model is constructed with the minimum long-term average cost rate of the high-speed rail sleeper as the target, the self-healing resource input and the sleeper replacement age as the decision variables, and the self-healing resource usage rate and the sleeper performance index as the constraints;

[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 rail sleeper data includes self-healing design principles, degradation and failure data, and failure thresholds.

[0013] Specifically, the self-healing mechanism and failure process of the sleeper are described according to the high-speed rail sleeper data, which includes using a random process to mathematically describe the self-healing mechanism and failure process of the high-speed rail sleeper, including distinguishing the different effects of type I and type II impacts on the sleeper, wherein type I impact can be self-healed by the self-healing resources embedded in the sleeper, type II impact cannot be self-healed, and the correlation between them is revealed.

[0014] Specifically, the self-healing mechanism and failure process of the high-speed rail sleeper are mathematically described using a random process, which includes:

[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 a perfect state and N represents a failure state;

[0016] The sleeper has M units of self-healing resources, and the sleeper will attempt self-healing every time interval Z, trying to transfer the degradation state from i(1≤i<K) to the adjacent degradation 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 degradation state i(1≤i<K), each self-healing attempt will transfer the self-healing resource consumption state from m(m∈H) to n(m≤n≤M) with probability η i,mn The self-healing resource consumption state is transferred from m(m∈H) to n(m≤n≤M), and

[0018] The occurrence of type I impact follows a homogeneous Poisson process with parameter λ1, and each impact has a certain probability γ i,j The sleeper is transferred from degradation state i to degradation state j, and

[0019] The type II impact occurs according to a homogeneous Poisson process with parameter λ 2, and the damage caused by each type II impact depends on the current degradation state of the sleeper. When the sleeper is in degradation state i, the damage caused by the gth type II impact is Y i,g , are independent and identically distributed random variables with cumulative distribution function and probability density function and When the damage caused by a type II impact exceeds the failure threshold D of the sleeper, the sleeper fails.

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

[0021]

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

[0023] Specifically, the self-recovery resource design decision model is solved by a search algorithm, including:

[0024] setting the thresholds of the self-recovery resource utilization rate and the steady-state availability, and the number of iterations; initializing the minimum long-term operation cost rate and the corresponding optimal self-recovery resource input and the best sleeper replacement age;

[0025] if the steady-state availability of the sleeper is not less than the threshold A min , calculating the average self-recovery resource utilization rate of the sleeper;

[0026] if the average self-recovery resource utilization rate of the sleeper is not less than the threshold U min , calculating the long-term average cost rate;

[0027] If the long-term average operating cost rate does not change after continuous multiple 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 continuous multiple iterations in the outer loop, the outer loop is stopped, and it is considered that the optimal solution has been approached or reached.

[0029] In another aspect, the present application provides a high-speed rail sleeper self-healing resource design system based on reliability, which comprises:

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

[0031] A model construction module is configured to construct a self-healing resource design decision model based on the self-healing mechanism and failure process, with the objective of minimizing the long-term operating 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 usage rate and the sleeper performance index as constraints;

[0032] A model solution module is configured to solve the self-healing resource design decision model by a search algorithm to obtain the optimal self-healing resource input amount and the optimal sleeper replacement age.

[0033] The present application has the following beneficial effects:

[0034] The present application fully considers the dual effects of performance improvement and cost increase brought by embedding self-healing resources in high-speed rail sleepers, and constructs an optimization model for self-healing resource design. The model realizes the dual optimization of self-healing resource input amount and sleeper replacement timing by minimizing the long-term operating cost rate of the sleeper under the dual constraints of self-healing resource usage rate and sleeper reliability index. The present application ensures the high reliability of high-speed rail sleepers while effectively controlling the operation and maintenance cost, achieving a perfect balance between the two. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 The flowchart of the method described in the present application patent;

[0036] Figure 2 The possible performance degradation sample path diagram of the high-speed rail sleeper;

[0037] Figure 3 The long-term average operating cost rate change trend of the high-speed rail sleeper;

[0038] Figure 4 The self-healing resource utilization rate change trend of the high-speed rail sleeper;

[0039] Figure 5 The steady-state availability change trend of the high-speed rail sleeper;

[0040] Figure 6 The structural diagram of the system described in the patent of the application. DETAILED DESCRIPTION

[0041] In order for those skilled in the art to better understand the technical scheme of the present application, the technical scheme in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor should belong to the scope of protection of the present application.

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

[0043] Embodiment 1

[0044] As Figure 1 shown, the embodiment of the present application provides a high-speed rail sleeper self-healing resource design method based on reliability, which comprises the following steps:

[0045] Step 1, obtaining high-speed rail sleeper data; according to the high-speed rail sleeper data, the self-healing mechanism and failure process of the high-speed rail sleeper are described.

[0046] Specifically, the high-speed rail sleeper data includes self-healing design principle, degradation failure data and failure threshold.

[0047] The high-speed rail sleeper involved in the embodiment of the present application is embedded with self-healing resources, which can randomly cope with two types of impacts: type I impact and type II impact. Among them, the damage caused by type I impact can be repaired spontaneously by the self-healing resources consumed by the sleeper; and type II impact will cause direct and irreversible damage to the system. The self-healing ability of the high-speed rail sleeper depends on the consumption of self-healing resources, and once the self-healing resources are exhausted, the sleeper will lose the self-healing ability. Both types of impacts can cause the sleeper to fail, thereby forming a competitive failure process.

[0048] Based on the above, in the embodiment, the self-recovery mechanism and failure process of the high-speed rail sleeper are described according to the high-speed rail sleeper data, including: using a random process to mathematically describe the self-recovery mechanism and failure process of the high-speed rail sleeper, including distinguishing the different effects of type I impact and type II impact on the sleeper, wherein type I impact can be self-recovered through the self-recovery resources embedded in the sleeper, type II impact cannot be self-recovered, and the correlation between them is revealed.

[0049] Further, the self-recovery mechanism and failure process of the high-speed rail sleeper are mathematically described using a random process, including:

[0050] Self-recovery resources and type I impact description

[0051] (1) The high-speed rail sleeper has K+1 degradation states 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 the number indicates the decline in the performance of the sleeper. 0 and K are 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 represent that the sleeper is in damage state i at time t.

[0052] (2) The occurrence of type I impact follows a homogeneous Poisson process {N1(t),t≥0} with parameter λ1, where N1(t) represents the number of type I impacts occurring in the time interval (0,t]. Each occurrence of type I impact will cause damage to the high-speed rail sleeper with a certain probability, causing the sleeper to move to a higher degradation state. Specifically, when the sleeper is in degradation state i (i∈S W ), the probability of the following type I impact causing the sleeper to move to degradation state j is γ i,j , and there is

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

[0054] (4) Corresponding to the initial embedded self-repairing resource amount, the high-speed rail sleeper has M+1 self-repairing resource consumption states, and the state space is H={0, 1,..., M}. When the sleeper is in the degradation state i (1≤i<K), each self-repairing attempt will consume self-repairing resources with a probability η i,mn , and the transition probability is . Note that η i,mm represents that the self-repairing resources fail to be effectively released due to some factors (for example, the performance level of the sleeper is too low), resulting in the failure of this self-repairing attempt. When the sleeper enters the consumption state M, it means that the self-repairing resources have been exhausted, and the sleeper no longer has self-repairing capability. Define H(t)=m to represent that the sleeper is in the consumption state m at time t.

[0055] Type II impact assumption

[0056] (1) Type II impact occurs according to a homogeneous Poisson process {N2(t), t≥0} with parameter λ2, and N2(t) represents the number of type II impacts occurring in the time (0, t]. The damage caused by each type II impact to the high-speed rail sleeper depends on the current degradation state of the sleeper. When the sleeper is in the degradation state i, the damage caused by the gth type II impact to the system is Y i,g . , which are independent and identically distributed random variables, and their cumulative distribution functions and probability density functions are and

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

[0058] It should be noted that the age replacement strategy of the high-speed rail sleeper in the embodiment of the present application sets a clear replacement criterion: once the running time of the sleeper reaches the preset threshold, or the sleeper fails during operation, it should be immediately replaced. In the two conditions, the first occurring condition is used as the criterion. Such a strategy aims to ensure the safety and reliability of the high-speed rail sleeper and avoid safety accidents caused by the aging or failure of the sleeper.

[0059] To better understand the failure process of the high-speed rail sleeper, Figure 2 two possible sample paths of the high-speed rail sleeper are given. As shown in Figure 2 , the transition of the degradation state of the high-speed rail sleeper occurs under the joint action of type I impact and the inherent self-repairing mechanism. Each self-repairing action will randomly consume a certain amount of self-repairing resources, so when the self-repairing resources are exhausted, the sleeper can no longer perform self-repairing. 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-repairing mechanism and failure process, a self-repairing resource design decision model is constructed with the minimum long-term average cost rate of high-speed rail sleepers as the target, the self-repairing resource input and sleeper replacement age as the decision variables, and the self-repairing resource usage rate and sleeper performance index as the constraints.

[0061] The embodiment of the present application defines the initial self-repairing resource input of high-speed rail sleepers, which is a key parameter. A larger self-repairing resource input can significantly improve the performance of sleepers and enhance their resistance to impact, but correspondingly, it will also bring higher self-repairing resource cost. On the contrary, a smaller self-repairing resource input can save cost, but it may sacrifice the performance of sleepers and increase the risk of failure after impact.

[0062] In order to balance the performance, cost and replacement frequency of sleepers, the present application proposes the demand for optimizing the two parameters of self-repairing resource input and sleeper replacement age. By comprehensively considering the safety benefits brought by performance improvement, the cost of self-repairing resources and the maintenance cost of replacing sleepers, an optimal solution can be found to make sleepers not only have the best performance but also control the cost within a reasonable range under the premise of safety.

[0063] Specifically, the present application patent will target at minimizing the long-term running cost rate of high-speed rail sleepers, and under the constraints of resource usage rate and sleeper performance index, the optimal self-repairing resource input M and sleeper replacement age τ are decided.

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

[0065]

[0066] E(C) represents the average total cost generated in an update cycle, and E(D) represents the average time length of an update cycle. E(D) is composed of the average running time E(T o ) of sleepers and the average replacement time E(M), that is,

[0067]

[0068] Let the random variable represent the time required for each replacement, and its cumulative distribution function is M(t). It is easy to know that In addition, let the random variable T represent the life of sleepers, and its cumulative distribution function, probability density function and reliability function distribution are F(t), f(t) and R(t). Under the age replacement strategy, the average running time of sleepers in an update cycle is

[0069]

[0070] Taking Laplace transform of equation (3) with respect to τ, we have

[0071]

[0072] Therefore, E(T o ) can be obtained by taking inverse Laplace transform of s -1 R * (s) with respect to s.

[0073] The total cost of high-speed rail sleeper in one renewal cycle includes the following five parts:

[0074] The cost of purchasing new sleeper C p , which does not include the cost of self-repairing resource investment;

[0075] The cost of self-repairing resource investment C m M, where C m represents the cost of per unit of self-repairing resource;

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

[0077] The cost of sleeper failure C f , which includes economic loss, safety loss and other losses caused by sleeper failure;

[0078] The maintenance cost of replacing sleeper where C r represents the cost of per unit of maintenance time.

[0079] Accordingly, the average total cost in one renewal cycle is

[0080]

[0081] Substituting equations (2)-(4) into equation (1), we can obtain the calculation formula of long-term operation cost rate, which is the objective function of the joint optimization model. To ensure effective use of resources and stable operation of the system, two constraints are added to the model. One is that the average self-repairing resource utilization rate cannot be lower than the given minimum value U min . Let r u (t) represent the self-repairing resource utilization rate at time t, then the constraint can be expressed as r u (E(T o ))≥U min . The other is that the steady-state availability A of sleeper must be greater than the set threshold Amin The steady-state availability can be calculated by dividing the average running time of the sleeper in an update cycle by the average length of an update cycle, i.e.

[0082]

[0083] Considering the real scenario, it is assumed that M and τ are non-zero positive integers. Therefore, according to the above analysis, the self-repairing resource design decision model is:

[0084]

[0085] where M and τ represent the self-repairing resource input and sleeper replacement age, respectively, C p is the purchase cost of a new sleeper, C m M represents the self-repairing resource input cost, C o E(T o ) represents the cost generated by the running of the sleeper, C f represents the cost generated by the failure of the sleeper, represents the maintenance cost generated by replacing the sleeper, E(T o ) and E(M) represent the average running time and average replacement time of the sleeper in an update cycle, respectively, R(τ) represents the reliability of the sleeper at time τ, r u (E(T o )) represents the average self-repairing resource utilization rate of the sleeper in an update cycle, U min represents the average self-repairing resource utilization rate threshold, A represents the steady-state availability of the sleeper, and A min represents the steady-state availability threshold.

[0086] In the process of constructing the self-repairing resource design decision model, the reliability R(t) of the high-speed rail sleeper and the self-repairing resource utilization rate r u (t) also need to be calculated.

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

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

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

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

[0091]

[0092] where, denotes the time when the a-th sleeper degradation state changes, S a and H a denotes the degradation state and resource consumption state of the sleeper at time C a . 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 renewal process The corresponding semi-Markov kernel is defined as V(t) = {V mn,ij (t); m, n e H; i, j e S}. There are

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

[0094] To obtain the analytical expression of R m,i (t) is the prerequisite for deriving R(t), and according to equation (7), the value of V m,i (t) is inevitably needed in the process of solving R mn,ij (t). Therefore, the calculation formula of V mn,ij (t) is first given by Lemma 1.

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

[0096]

[0097] Proof: According to the evolution rules of system degradation state and resource consumption state, the following important conclusions can be obtained:

[0098] For any i, j e 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 transfer to a higher level.

[0099] For any m e 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 e 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 move the system degradation state one unit better.

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

[0102] Case 1: S0 = i (0≤i

[0103] In this case, the initial self-repairing resource state of the sleeper is M, which means that the embedded self-repairing resource has been consumed and the sleeper no longer has self-repairing ability. Therefore, the change of the sleeper degradation state can only be caused by a certain I-type impact. Accordingly, there is

[0104]

[0105] where N c represents the number of I-type impacts occurring before the first change of the degradation state. Φ a represents the time of the a-th I-type impact. Since the arrival of the I-type impact obeys a homogeneous Poisson process, Φ a is a random variable obeying a gamma distribution with shape parameter a and scale parameter λ1, and its PDF is

[0106]

[0107] CDF is Q a (t) = P{Φ a ≤ t}.

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

[0109] In this case, the initial degradation state of the sleeper is 0, so the first transition can only be to a higher degradation state. Similar to Case 1, there is

[0110]

[0111] Case 3: S0 = i (1≤i

[0112] In this case, the sleeper successfully completes one self-repairing action and consumes (n-m) units of self-repairing resource. According to the assumption condition, the sleeper will perform a self-repairing attempt every time interval Z. Therefore, before time t, at least one self-repairing attempt has occurred. Let Υ b represent the time of the b-th self-repairing attempt, since Z obeys an exponential distribution with parameter β, Υ b obeys a gamma distribution with shape parameter b and scale parameter β. Its cumulative distribution function is denoted as G b (t) and g b (t).

[0113]

[0114] Case 4: S0 = i (1≤i<K), H0 = m (0≤m<M); S1 = j (i<j≤K), H1 = m.

[0115] In this case, the sleeper fails to complete a self-recovery action successfully. Its degradation state changes because of a Type I impact. Therefore, there exists

[0116]

[0117] Right side, first term: Z > Φ a which means that before the first self-recovery attempt, the sleeper has already shifted to a higher degradation state because of a Type I impact. Therefore, there exists

[0118]

[0119] Right side, second term: Z ≤ Φ a which means that before the sleeper's degradation state changes, there exists at least one self-recovery attempt, but all self-recovery attempts fail because the self-recovery resource is not released successfully. Therefore, there exists

[0120]

[0121] Combining the two terms above, we have

[0122]

[0123] Taking the Laplace transform of equations (8) to (11) with respect to t, we obtain Lemma 1.

[0124] Based on Lemma 1, Theorem 1 gives the conditional reliability R m,i (t) after Laplace transform. Theorem 1: Conditional reliability R m,i (t) after Laplace transform. Theorem 1: Conditional reliability R

[0125]

[0126] where,

[0127] Proof: We discuss the two terms on the right side of equation (7) separately.

[0128] Right side, first term: Event {C1 > t} means that the sleeper's degradation state does not change in the interval (0, t]. Therefore, there exists

[0129]

[0130] where P{Y(t) < D | C1>t, S0=i, H0=m} denotes the probability that the maximum value of the II-type impact damage suffered by the sleeper in the interval (0, t] is less than the threshold value D, given that the initial resource consumption state is m, the degradation state is i and has remained unchanged until time t. Its expression is

[0131]

[0132] The second term on the right side: when C1≤t, there is

[0133]

[0134] Therefore, we can get

[0135]

[0136] Taking the Laplace transform of the above equation with respect to t, we get Theorem 1.

[0137] Define the following matrix:

[0138]

[0139] Then equation (12) can be written in matrix form as

[0140] R * (s) = Θ * (s) - Γ * (s)1 (M+1)×(K+1) + Φ * (s)Ω * (s)R * (s),

[0141] After rearrangement, we get

[0142] R * (s) = (I - Φ * (s)Ω * (s) )(Θ * (s) - Γ * (s)1 (M+1)×(K+1) ). (13)

[0143] where 1 (M+1)×(K+1) is an (M+1)(K+1)-dimensional column vector with all elements equal to 1.

[0144] Let ζ = (ζ0, ζ1, …, ζ M ) denote the initial distribution vector of the self-recovery resource consumption state. Since 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 represented as α = (α0, α1, …, α K-1). According to formula (13), the reliability of the sleeper at time t is

[0145] R * (s) = θR * (s), (14)

[0146] where θ = (ζ0α, ζ1α, …, ζ M α). The Laplace inverse transform of formula (14) with respect to s can obtain the reliability of the sleeper at time t.

[0147] Specifically, the self-recovery resource utilization rate r u (t) is calculated as follows:

[0148] The self-recovery resource utilization rate r u (t) at time t is defined as the proportion of the consumed self-recovery resource amount to the initial self-recovery resource amount of the high-speed rail sleeper, and its mathematical expression is

[0149]

[0150] E[H(t)] represents the average consumption of self-recovery resources of the sleeper at time t,

[0151]

[0152] To solve the value of P{H(t) = n}, a new conditional probability W mn,ij (t) is defined, and its expression is

[0153] W mn,ij (t) = P{H(t) = n, S(t) = j | So = i, Ho = m}, i, j ∈ S; m, n ∈ E.

[0154] W mn,ij (t) represents the probability of the degradation state being j and the resource consumption state being 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 the expression of the Laplace transform of W mn,ij (t).

[0155] Theorem 2: The Laplace transform of W mn,ij (t) with respect to t is

[0156]

[0157] Proof: It is easy to know 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, the derivation of W mn,ij (t) needs to consider the following four cases.

[0158] Case 1: S0 = i (0≤i

[0159] Based on whether the first time of degradation state change C1 is earlier than time t, W mm,ij (t) can be further written as

[0160] W mm,ii (t) = P{H(t) = m, S(t) = i | S0 = i, H0 = m}

[0161] = P{H(t) = m, S(t) = i, C1 > t | S0 = i, H0 = m}

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

[0163] The first term on the right side: C1 > t indicates that the first time of degradation state change is later than time t, thus at time t the system is still in the initial degradation state and resource consumption state, and there is

[0164]

[0165] The second term on the right side: C1≤t indicates that the first time of degradation state change is earlier than time t. To ensure that at time t the system is still in the initial degradation state and resource consumption state, the sleeper must fail due to the II type impact before C1, i.e. Y(C1) > D. There is

[0166]

[0167] Therefore, it can be obtained that

[0168]

[0169] Case 2: S0 = i (0≤i

[0170] In case 2, the resource consumption state has changed, which means that the degradation state must also have changed before time t, thus there is C1≤t. Based on this,

[0171]

[0172] Case 3: S0 = i (0≤i

[0173] S(t) = K indicates that the sleeper has entered the degradation state at time t and failure has occurred. After this failure occurs, the system degradation state and resource consumption state no longer change.

[0174]

[0175] where P{H(t) = n, S(t) = K | S1 = K, H1 = n, C1 = x} = 1, and for e ≠ n, P{H(t) = n, S(t) = K | S1 = K, H1 = e, C1 = x} = 0.

[0176] P{H(t) = n, S(t) = K | S1 = K, H1 = e, C1 = x} = 0.

[0177] Case 4:

[0178] S0 = i (0 ≤ i < K), H0 = m (0 ≤ m ≤ M); S(t) = j (0 ≤ j < K, j ≠ i), H(t) = n (m ≤ n ≤ M).

[0179]

[0180] Taking the Laplace transform of equations (16) to (19) with respect to t gives Theorem 2. To solve for W(t), define the following matrices: mn,ij

[0181] where where

[0182]

[0183] where

[0184]

[0185] The equations in Theorem 2 can be written in matrix form as

[0186] Rearranged as

[0187]

[0188] The value of W(t) is obtained by taking the inverse Laplace transform of equation (20).

[0189] From equation (20), we have

[0190]

[0191] where p n ​is a (K+1)(M+1) dimensional column vector, whose n(K+1)+1, n(K+1)+2,..., (n+1)(K+1) elements are 1, and the rest are 0. The average utilization rate of the self-repairing resource at time t can be obtained by substituting the value of P{H(t)=n} calculated into formula (15).

[0192] Step 3, solving the self-repairing resource design decision model by a search algorithm to obtain the optimal self-repairing resource input and the optimal sleeper replacement age.

[0193] In the embodiment of the application, solving the self-repairing resource design decision model by a search algorithm comprises: setting threshold values of self-repairing resource utilization rate and steady-state availability, and iteration times; initializing the minimum long-term operation cost rate, and the corresponding optimal self-repairing resource input and optimal sleeper replacement age; if the steady-state availability of the sleeper is not less than the threshold value A min , calculating the average self-repairing resource utilization rate of the sleeper; if the average self-repairing resource utilization rate of the sleeper is not less than the threshold value U min , calculating the long-term average cost rate; if the long-term average operation cost rate does not change after continuous multiple iterations in the inner loop, stopping the inner loop and performing the outer loop; if the long-term average operation cost rate does not change after continuous multiple iterations in the outer loop, stopping the outer loop, and considering that the optimal solution has been approached or reached.

[0194] Specifically, the detailed implementation process of the search algorithm is shown in Table 1.

[0195] Table 1

[0196]

[0197]

[0198] In order to better understand the technical solutions of the application, the following will be described in detail with a specific high-speed rail sleeper as an example.

[0199] Consider a high-speed rail sleeper put into use at time 0, which will be randomly affected by two types of impacts during operation: type I impact and type II impact.

[0200] The occurrence of type I impact obeys a homogeneous Poisson process with a 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 degradation state i∈S WThe state transition probabilities induced by Type I shock are given in Table 2. For example, when the sleeper is in the degraded state 1, there is a certain probability to transit to other degraded states or remain in the original state due to Type I shock. When the sleeper enters the degraded state 5, it is considered to have failed.

[0201] The occurrence of Type II shock also obeys the homogeneous Poisson distribution, but its parameter is λ2= 0.1. The damage caused by each Type II shock to the sleeper depends on the current degraded state of the sleeper. Under different degraded states, it is assumed that the damage caused by Type II shock obeys the normal distribution with different mean and variance, i.e. 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, ∞}. Meanwhile, when the damage caused by a Type II shock exceeds the threshold D = 1.5, the sleeper fails.

[0202] Table 2 γ ij (i∈S W ,j∈S,i≤j) of the value

[0203]

[0204]

[0205] Assume that the cost parameter is C p = 4, C f = 20, C m = 0.5, C o = 0.2, C r = 0.1. According to this, the long-term average operation cost rate of the sleeper changes with the self-recovery resource input M and the replacement age τ as shown in Figure 3 Meanwhile, according to the formula (15), (5), the change trend of the self-recovery resource utilization rate and the steady-state availability of the sleeper can be calculated as shown in Figure 4 and Figure 5 .

[0206] In the self-recovery resource design decision model, it is required that the average self-recovery resource utilization rate cannot be less than the threshold U min = 0.65, and the steady-state availability of the sleeper cannot be less than A min = 0.8. According to the optimization algorithm in Table 1, the iteration number is set as IterationNum = 50, and accordingly the minimum long-term operation cost rate is ω * = 1.85692, the optimal self-recovery resource input is M * = 4, and the sleeper replacement age is τ * = 12.

[0207] Example 2

[0208] like Figure 6 As shown, this embodiment of the invention provides a reliability-based high-speed railway sleeper self-healing resource design system, which includes:

[0209] An initialization module is used to acquire high-speed railway sleeper data and characterize the self-healing mechanism and failure process of the high-speed railway sleepers based on the high-speed railway sleeper data;

[0210] The model building module is used to construct a self-healing resource design decision model based on the self-healing mechanism and failure process, with the goal of minimizing the long-term operating cost rate of high-speed railway sleepers, the amount of self-healing resource input and the age of sleeper replacement as decision variables, and the utilization rate of self-healing resources and sleeper performance indicators as constraints.

[0211] The model solving module is used to solve the self-healing resource design decision model through a search algorithm to obtain the optimal amount of self-healing resources and the optimal sleeper replacement age.

[0212] It should be understood that the reliability-based high-speed railway sleeper self-healing resource design system provided in this embodiment of the invention is based on the same inventive concept as the reliability-based high-speed railway sleeper self-healing resource design system provided in the above embodiments. For more specific working principles of each module in this embodiment of the invention, please refer to the above embodiments, which will not be repeated in this embodiment.

Claims

1. A high-speed rail sleeper self-healing resource design method based on reliability, characterized in that, The application relates to a self-recovery resource design decision-making method for high-speed railway sleepers. The application comprises the following steps: The self-recovery mechanism and failure process of the high-speed railway sleeper are mathematically described by using a random process, including distinguishing the different influences of type I impact and type II impact on the sleeper, wherein the type I impact can be self-recovered by the self-recovery resource embedded in the sleeper, the type II impact cannot be self-recovered, and the correlation between the two is revealed; specifically, the sleeper has K+1 degradation states corresponding to the cumulative damage caused by the type I impact, and the state space is S={0, 1, 2,..., K}, wherein 0 represents a perfect state and N represents a failure state; There are M units of self-recovery resources in the sleeper, and the sleeper will perform a self-recovery attempt every time interval Z, trying to transfer the degradation state from i (1<=i A self-recovery resource design decision-making model is constructed based on the self-recovery mechanism and failure process, with the minimum long-term average cost rate of the high-speed railway sleeper as the target, the self-recovery resource input and the sleeper replacement age as the decision variables, and the self-recovery resource utilization rate and the sleeper performance index as the constraints. The sleeper has M+1 self-healing resource consumption states, and the state space is H = {0, 1,..., M}. When the sleeper is in a degradation state i, 1≤i<K, each self-healing attempt will move to state i+1 with probability η i,mn The self-healing resource consumption state is moved from m, m∈H, to n, m≤n≤M, and has The occurrence of type I impacts obeys a homogeneous Poisson process with parameter λ1, and each impact occurs with probability γ i,j causes the sleeper to move from a degradation state i to a degradation state j, and has The type II impact occurs according to a homogeneous Poisson process with parameter λ 2, 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 with cumulative distribution function and probability density function and When the damage caused by a type II impact exceeds the failure threshold D that the sleeper can withstand, the sleeper fails. The self-recovery resource design decision-making model is as follows: The optimal self-recovery resource input and the optimal sleeper replacement age are obtained by solving the self-recovery resource design decision-making model through a search algorithm. where M and τ represent the self-repairing resource input and the sleeper replacement age, respectively, C p represents the purchase cost of new sleepers, C m M represents the self-repairing resource input cost, C o E(T o ) represents the cost generated by the sleeper operation, C f represents the cost generated by the sleeper failure, represents the maintenance cost generated by the sleeper replacement, E(T o ), E(M) represent the average operation time and the average replacement time of the sleeper within one replacement cycle, respectively, R(τ) represents the sleeper reliability at time τ, r u (E(T o )) represents the average self-repairing resource utilization of the sleeper within one replacement cycle, U min represents the average self-repairing resource utilization threshold, A represents the steady-state availability of the sleeper, A min represents the steady-state availability threshold; The high-speed railway sleeper data includes self-recovery design principles, degradation and failure data, and failure thresholds.

2. The high-speed rail sleeper self-healing resource design method based on reliability according to claim 1, characterized in that, Solving the self-recovery resource design decision-making model through a search algorithm comprises the following steps:

3. The high-speed rail sleeper self-healing resource design method based on reliability according to claim 1, characterized in that, Thresholds of self-recovery resource utilization rate and steady-state availability, and iteration times are set; the minimum long-term running cost rate and the corresponding optimal self-recovery resource input and optimal sleeper replacement age are initialized; If the long-term average running cost rate does not change after continuous multiple iterations in the inner loop, the inner loop is stopped, and the outer loop is performed; if the steady-state availability of the tie is not less than a threshold value A min then calculating the average self-healing resource utilization of the tie; If the average self-healing resource utilization of the track tie is not less than the threshold value U min then calculate the long-term average cost rate; If the long-term average running cost rate does not change after continuous multiple iterations in the outer loop, the outer loop is stopped, and it is considered that the optimal solution has been approached or reached. The application comprises the following steps:

4. A reliable-based high-speed rail sleeper self-healing resource design system using the design method of any one of claims 1-3, characterized in that, An initialization module is used to obtain high-speed railway sleeper data and describe the self-recovery mechanism and failure process of the high-speed railway sleeper according to the high-speed railway sleeper data; A model construction module is used to construct a self-recovery resource design decision-making model based on the self-recovery mechanism and failure process, with the minimum long-term running cost rate of the high-speed railway sleeper as the target, the self-recovery resource input and the sleeper replacement age as the decision variables, and the self-recovery resource utilization rate and the sleeper performance index as the constraints; A model solving module is used to solve the self-recovery resource design decision-making model through a search algorithm, and obtain the optimal self-recovery resource input and the optimal sleeper replacement age. ​

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