A Method for Reliability Assessment and Maintenance Strategy Optimization of Door Systems Based on pH Distribution

Abstract

This invention provides a method for reliability assessment and maintenance strategy optimization of vehicle door systems based on the PH distribution. The method includes: acquiring fault data recorded by vehicle repair departments; estimating PH distribution parameters based on the dwell time of components in different states within the door system following a PH distribution; obtaining the state set of components in the door system based on the PH distribution parameters; constructing the state transition matrix of the components in the door system; generating a general generating function for the door system; constructing the reliability structure of the door system; obtaining the output performance and maintenance cost of the door system; establishing an optimization objective function for the maintenance strategy of the door system with the goals of minimizing the maintenance cost rate and maximizing the expected output performance; solving the optimization objective function using the NSGA-II algorithm based on dynamic congestion distance; and obtaining the optimal maintenance strategy for the door system. This invention can analyze the reliability of vehicle door systems and optimize maintenance strategies for door systems with both minimum cost rate and maximum output performance as dual objectives.

Description

Technical Field

[0001] This invention relates to the field of computer application technology, and in particular to a method for reliability assessment and maintenance strategy optimization of vehicle door systems based on PH (Phase-type distribution). Background Technology

[0002] With the continuous enhancement of my country's national strength, the scale of rail transit has also expanded significantly. Therefore, higher demands are placed on the safety and reliability of rail transit operations. According to statistics on vehicle malfunctions, the door system is one of the systems with a high failure rate. Based on three years of malfunction statistics from a certain depot, door system failures accounted for 37% of the total. Due to the frequent opening and closing of vehicle doors, components suffer damage and aging, making doors prone to failure. Doors are crucial passageways for passengers boarding and alighting; if doors fail, it will affect train operation, causing delays and even jeopardizing passenger safety. Therefore, it is essential to study the reliability of the door system and develop reasonable maintenance procedures to meet maintenance needs. Currently, vehicle system maintenance mainly follows the maintenance procedures of individual operating companies, some of which are no longer suitable for the current operational situation. Based on actual operating data, the system status and reliability can be analyzed to improve the system's maintenance cycle and meet the company's cost reduction and efficiency improvement goals.

[0003] Currently, existing technologies for optimizing the reliability or maintenance strategies of vehicle door systems mostly rely on statistically analyzing the time intervals between recorded faults to fit a certain distribution that the system follows, thereby further analyzing system reliability. This method requires a large amount of data to ensure the accuracy of the fitted distribution.

[0004] The disadvantages of the existing methods for reliability assessment and maintenance strategy optimization of door systems include:

[0005] Current technologies for optimizing the reliability or maintenance strategies of vehicle door systems do not consider the relationships between components or treat the system as a whole. A vehicle door system is a complex, multi-state system; its components exhibit various states during operation. Composed of multiple components such as door controllers, door locks, and position switches, it forms a multi-state system. The reliability changes of the system can be analyzed by analyzing the transitions between these states. Current system maintenance often focuses on only one objective, such as maintenance time or cost rate, with less consideration given to multiple objectives. Maintenance strategies that consider multiple objectives based on actual operational needs are more likely to meet the demands of system maintenance.

[0006] This method rarely considers the multi-state characteristics of the system and the logical relationship of the system structure when analyzing the door system. It only fits the time distribution of the system without failure based on historical fault data, which cannot represent the performance output function of the system in different states. Moreover, the fitting generally assumes that the time of the components follows a certain distribution. If the actual problem background is slightly different from the assumption, it will reduce the accuracy and practicality of the analytical model to a certain extent. Furthermore, when the amount of data is small, the fitting is prone to bias, resulting in inaccurate model. Summary of the Invention

[0007] The embodiments of the present invention provide a method for reliability assessment and maintenance strategy optimization of a vehicle door system based on pH distribution, so as to effectively obtain the optimal maintenance strategy for the vehicle door system.

[0008] To achieve the above objectives, the present invention adopts the following technical solution.

[0009] A method for reliability assessment and maintenance strategy optimization of a vehicle door system based on pH distribution includes:

[0010] Fault data recorded by the vehicle repair department is obtained. Assuming that the dwell time of components in the door system in different states follows a PH distribution, the deterministic annealing expectation-maximization (DAEM) algorithm is used to estimate the PH distribution parameters.

[0011] Based on the PH distribution parameters, the state set of the components in the door system is obtained, the state transition matrix of the components in the door system is constructed, and the general generating function of the door system is generated based on the state transition matrix of the components in the door system.

[0012] Construct a reliability structure for the vehicle door system, obtain the performance output function of the vehicle door system based on the general generation function and reliability structure of the vehicle door components, and obtain the output performance and maintenance cost of the vehicle door system based on the performance output function of the vehicle door system.

[0013] With the goals of minimizing maintenance cost rate and maximizing expected output performance, an optimization objective function for the maintenance strategy of the door system is established. The NSGA-II algorithm based on dynamic congestion distance is used to solve the optimization objective function to obtain the optimal maintenance strategy for the door system.

[0014] Preferably, the acquisition of fault data recorded by the vehicle repair department assumes that the dwell time of components in the door system under different states follows a PH distribution, and the DAEM algorithm is used to estimate the PH distribution parameters, including:

[0015] Based on the fault data recorded by the vehicle repair department, the fault data is classified and statistically analyzed according to different components. The dwell time of each component in different states is calculated according to the state of the components. Assuming that the dwell time of the components in different states follows a PH distribution, the DAEM algorithm is used to estimate the PH distribution parameters to obtain the dwell time of the components in each state, and the observed fault dataset D is constructed.

[0016] The pH distribution is the time distribution of a Markov process before it enters the absorption state m+1 in the state space {1,2,…,m,m+1}, denoted as PH(τ,T), (τ,τ) m+1 Let τ = (τ1, τ2, ..., τn) be the initial probability vector of the Markov process. m ), satisfying τ+τ m+1 =1, the infinitesimal generator of this process is:

[0017]

[0018] T is the state transition rate matrix, a non-singular m-order square matrix satisfying Te+T 0 =0,T 0 Let f(·) be the transition probability from any state to the absorption state m+1, and let f(·) be the probability density function and the cumulative distribution function F(·).

[0019] f(x)=τexp(Tx)T 0 x≥0 (2)

[0020] F(x)=1-τexp(Tx)e,x≥0 (3)

[0021] T and T in the distribution 0 The production matrix and the transition rate vector from the transient state to the absorption state, respectively, are represented as follows:

[0022]

[0023] T 0 =(ξ1 ξ2…ξ) m ) T (5)

[0024] D is the observed fault dataset recorded by the vehicle repair department. The observed fault dataset D consists of K samples that satisfy the PH distribution, D=(t1,…,t k Assume 0 <t1<...<t k Consider that the observed fault dataset D follows an m-order PH distribution;

[0025] Unobserved statistics are defined according to the EM algorithm:

[0026] Indicator random variable, indicating that the state of the k-th sample starts from order i;

[0027] The dwell time of the kth sample in the i-th state;

[0028] The kth sample t k The number of phase transitions from state i to state j;

[0029] Y i [k] : Indicator random variable, representing the phase i observed in the k-th sample. The likelihood estimation function can be expressed as:

[0030]

[0031] in, θ=(τ1,...,μ 1,2 The elements in θ (ξ1, ..., ξ2, ...) represent the parameter values ​​that need to be estimated for the pH distribution. Introducing the inversion factor, the temporary parameter value θ' of θ is obtained using the following formula.

[0032]

[0033] In the formula v β It is a constant.

[0034] The thermodynamic free energy function estimated by the pH distribution parameters is:

[0035]

[0036] in It is the maximum likelihood estimation function of the PH distribution;

[0037] Based on the transformed parameters, the E-step of the DAEM algorithm is executed, introducing... and Represented as:

[0038]

[0039] in The random variable representing the pH transition. The pH distribution transformation process can be represented as follows:

[0040]

[0041] For the thermodynamic free energy function F β After minimizing (θ), and introducing transformation parameters, the expected correlation of the fitting parameters for the PH distribution data is:

[0042]

[0043] Then, by performing M steps, the parameter estimates of the PH distribution are obtained as follows:

[0044]

[0045] Where T is a random variable of the PH distribution, and θ' is a temporary parameter vector. Given the initial values ​​of β and θ, the temporary parameter of θ is obtained through equation (7). The updated θ value is calculated based on the E-step and M-step steps described above. The β value is increased and the θ value is iterated repeatedly until β = 1. The expected value of the unobserved variable is calculated using equation (11), and then the estimated PH distribution parameter value τ is calculated using equation (12). i μ i,j and ξ i .

[0046] Preferably, the step of obtaining the state set of components in the door system based on the PH distribution parameters and constructing the state transition matrix of the components in the door system includes:

[0047] The component is assigned a state set S = {1,2,…,n,n+1} based on its actual state. The states in set S are categorized into three types according to the component's operational state:

[0048] (1) Healthy state, state set G = {1,2,...,k};

[0049] (2) Sub-health state, where the state set B = {k+1,k+2,...,n};

[0050] (3) Maintenance status, the status is set to F={n+1};

[0051] Assume that the dwell time of a component in states G and B follows a PH distribution, denoted as PH(α,T) and PH(β,V) respectively. The system state transitions from state G to state B. The system's corrective maintenance time follows PH(γ1,L1), the low-level preventive maintenance time follows PH(γ2,L2), the high-level preventive maintenance time follows PH(γ3,L3), and the replacement maintenance time follows PH(δ,M).

[0052] Introducing a degradation factor ρ, the pH distributions of the component's residence time in state G and state B are respectively PH(α,ρ). h T) and (β,ρ) h(V), taking ρ > 1, group the states of the system into macroscopic states. Let Ω denote the component state space, then Ω = {Α, Γ, Ε, Η, Λ, Ψ}. The macro-states in the state space Ω respectively correspond to the healthy state, sub-healthy state, corrective maintenance state, low-level preventive maintenance state, high-level preventive maintenance state, and replacement state of the component. Define {(h, l, i1, i2, c1, c2, c3, ε): 1 ≤ l < Np, 1 ≤ h < Nr, 1 ≤ i1 ≤ m1, 1 ≤ i2 ≤ m2, 1 ≤ c1 ≤ u1, 1 ≤ c2 ≤ u2, 1 ≤ c3 ≤ u3, 1 ≤ ε ≤ w}, where h and l are the numbers of low-level and high-level preventive maintenance performed on the component, i1, i2 represent the healthy state and sub-healthy state, c1, c2, c3, and ε respectively represent the stages of the component in the corrective maintenance, low-level preventive maintenance, high-level preventive maintenance, and replacement states. The phases of these macroscopic states satisfy:

[0053] Α = {(h, l, i): 1 ≤ l ≤ Np, 1 ≤ h < Nr, 1 ≤ i1 ≤ m1},

[0054] Γ = {(h, l, i): 1 ≤ l ≤ Np, 1 ≤ h < Nr, 1 ≤ i2 ≤ m2},

[0055] Ε = {(h, l, i, c1): 1 ≤ l ≤ Np, 1 ≤ h < Nr, 1 ≤ i2 ≤ m2, 1 ≤ c1 ≤ u1},

[0056] Η = {(h, l, i, c2): 1 ≤ l < Np, 1 ≤ h < Nr, 1 ≤ c2 ≤ u2},

[0057] Λ = {(h, l, i, c3): l = Np, 1 ≤ h < Nr, 1 ≤ c3 ≤ u3},

[0058] Ψ = {(h, l, i, ε): l = Np, h = Nr, 1 ≤ ε ≤ w}.

[0059] Construct the infinitesimal generator matrix of the component according to the state transition process of the component;

[0060] (1) The state transition matrix of the component in the working state is denoted as Θ1, which respectively includes the internal transition of the healthy state, the transition of the sub-healthy state, and the transition from the healthy state to the sub-healthy state;

[0061]

[0062] In the formula, p ΑX represents the probability of transferring from the macro-state Α to any macro-state X. The transition probabilities from the macro-state Α to the macro-states Γ, Ε, Η, and Λ satisfy p ΑΓ + p ΑΕ + p ΑΗ + p ΑΛ=1, macrostate Γ transitions to other macrostates E, H, and Λ with transition probabilities satisfying p ΓΕ +p ΓΗ +p ΓΛ =1;

[0063] The PH distribution is a Markov process defined in the state space, where the change in the probability vector p of a component in a healthy state satisfies:

[0064]

[0065] Let α be the initial probability of transitioning from a healthy state to a preventive maintenance state at time t, and let ∑p be the probability of transitioning from a healthy state to a preventive maintenance state at time t. i (t), p i It is an element of p(t). Two levels of preventive maintenance cannot occur simultaneously, when p ΑΗ or p ΑΛ When determined, the other value is 0, p at time t. ΑΕ λ(1-∑p) i (t)), p ΑΓ For (1-λ)(1-∑p) i (t)), where λ is the probability that a healthy state is absorbed and transitions to a faulty state. The transition of a component from a sub-healthy state satisfies dp(t) / dt=p(t)V, and the initial state probability is β, p ΓH or p ΓΛ for

[0066] ∑p i (t), p ΓΕ 1-∑p i (t);

[0067] (2) The state transition matrix from healthy state and sub-healthy state to low-level preventive maintenance state is denoted as matrix Θ2;

[0068]

[0069] (3) The state transition matrix of the component from healthy state and sub-healthy state to corrective maintenance state is Θ3;

[0070]

[0071] (4) The state transition matrix for components that have completed low-level preventive maintenance and whose performance has improved to a healthy state and a sub-healthy state is Θ4.

[0072]

[0073] The initial probabilities of a component completing l low-level preventive maintenance and entering the l+1 low-level preventive maintenance interval are denoted as α(l) and β(l), respectively. Equation (14) calculates the probability of health status change at time t, where the element value of α(l) is p. i / ∑p i ;

[0074] (5) The component transfer matrix Θ5 during low-level preventive maintenance is as follows:

[0075]

[0076] (6) The state transition matrix from the corrective maintenance state to the healthy state and the sub-healthy state is represented by matrix Θ6;

[0077]

[0078] (7) The state transition matrix within the corrective maintenance state is:

[0079] Based on the transmission process of the component between macro states, the infinitesimal generation matrix Q(h) of the component in the h-th advanced preventive maintenance interval is obtained;

[0080]

[0081] In the formula, lX represents the macro state X of the component after l low-level preventive maintenance, macro state A and Γ both represent the component in working state, and working state is represented by W;

[0082] (8) The state transition matrix of the component from the working state to the advanced preventive maintenance state is Θ7;

[0083]

[0084] (9) After advanced preventive maintenance, the component transitions to a healthy state, and the state transition matrix is ​​Θ8;

[0085]

[0086] (10) The internal state transition matrix of the component in advanced preventive maintenance state is as follows:

[0087] (11) After the component has undergone Nr-level advanced preventive maintenance, or after the component has been replaced or returned to the factory, the state transition matrix is ​​Θ9.

[0088]

[0089] (12) The transition matrix of the component during the replacement and maintenance state is as follows: After replacement, the component is in a new state, and the transition matrix to the healthy state is M. 0 α;

[0090] In the above process, Θ1-Θ9 are the state transition matrices of two adjacent states that may occur in the operation of the components in the door system. The complete state transition matrix Q of the component is obtained through the matrices Θ1-Θ9.

[0091] Preferably, the step of generating a general generating function for the door system based on the state transition matrix of the components in the door system includes:

[0092] Consider the infinitesimal generation matrix Q of the advanced preventative maintenance component:

[0093]

[0094] The general generating function q of the component at time t is expressed as:

[0095]

[0096] Where p jq (t) represents the component at time t with performance g. q The probability of (j);

[0097] Component q obeys PH(ζ) in every macroscopic state q Q q The initial probability is ζ. q =(α q Let v = (0,0,…,0) jq Indicates the performance of component q in each phase. q (j), p jq (t)=v jq (t)e, denoted as V q (t)=(v 1q (t),...,v fiq (t));

[0098] According to the Chapman-Kolmogorov equation, the probability of the performance level of component q at time t+Δt can be divided into the following probability combinations:

[0099] ③ The performance of component q at time t is g q (j), and the probability that the performance has not changed is (1+Q) q (jj)Δt)v jq (t) T ;

[0100] ② Component q is in performance g at time t. q (b) The performance transfers to g over time Δt. qThe probability of (j) is:

[0101]

[0102] Therefore:

[0103]

[0104] Q q (bj) is the component from the performance g q (b) Transfer to performance g q The transition probability matrix of (j) is expressed as:

[0105]

[0106] When the initial condition is v q (0)=ζ q When the solution to the differential equation is:

[0107] v q (t)=ζ q exp(Q q t) (28)

[0108] For a complex system with N components, the z-transform of the system is denoted as:

[0109]

[0110] Where U(z) is the system function f(u1(z,t),u2(z,t),…,u N (z,t)); g s p are the possible state values ​​of f(·); s It is the probability corresponding to f(·).

[0111] Based on the state transition matrix of the door system, the general generating functions of each key component of the door system are constructed using the improved general generating function method through equations (26)-(28). The general generating function of the door system is constructed through equation (29). Based on the general generating function of the door system, various performance states of the door system are obtained, and then the performance output function of the door system is obtained.

[0112] Preferably, the construction of the reliability structure of the vehicle door system, obtaining the performance output function of the vehicle door system based on the general generation function of the vehicle door components and the reliability structure, and obtaining the output performance and maintenance cost of the vehicle door system based on the performance output function of the vehicle door system, includes:

[0113] The train is configured with multiple carriages, each containing multiple passenger doors. M represents a motor vehicle, and T represents a trailer. Passenger doors are controlled by door control units. Each carriage has one main door control unit, and the rest are local door control units. Within each carriage, the main door control unit transmits the door status information to the multi-function vehicle bus, and then forwards the door information to the central control unit, enabling data exchange between train door communication information. The actions of each component in the door system are controlled by the DCU (Digital Control Unit). Each transport control door system (MDCU) transmits signals from other LDCUs, and the MDCUs are connected in parallel.

[0114] Construct a general generation function for each component in the door system, and define the performance levels of the healthy state, sub-healthy state, and maintenance state of the component as 1, 0.5, and 0, respectively. Each component in the door system belongs to three subsystems: electronic control unit, drive guidance device, and locking device. For a subsystem, if more than half of the components are in a sub-healthy state, the subsystem is considered to be in a sub-healthy state; if any component is in a maintenance state, it is considered to be in a maintenance state.

[0115] According to the performance output function of the door system, if all three subsystems are in a healthy state, the system is considered to be in a healthy state, and the performance is recorded as 1; if any subsystem is in a sub-healthy state, the door system is considered to be in a sub-healthy state, and the performance is recorded as 0.5. When the system is in maintenance mode, the performance is represented as 0.

[0116] Preferably, the optimization objective function for establishing the maintenance strategy of the door system, which aims to minimize the maintenance cost rate and maximize the expected output performance, includes:

[0117] The optimization objective of the maintenance strategy for the vehicle door system is to maximize expected performance and minimize the cost rate, with the cost of each corrective maintenance being M. cf The cost of basic preventive maintenance is M. cl The cost of advanced preventive maintenance is M. ca The cost of replacement and repair is M. cr p w (t) and p f (t) represent the probabilities of the system being in a working state and a maintenance state, respectively. The objective function for optimizing the maintenance strategy of the door system is as follows:

[0118]

[0119]

[0120] st

[0121]

[0122] p w(t) and p f (t) represents the probability of the system being in a working state and a maintenance state. Equation (30) represents the objective function to maximize the expected performance output. The performance and probability of the door system are given by Equation (29). Equation (31) is the objective function to minimize the maintenance cost rate. Equation (32) is the reliability constraint. R l This represents the lower limit of system reliability.

[0123] Preferably, the step of using the NSGA-II algorithm based on dynamic congestion distance to solve the optimization objective function and obtain the optimal maintenance strategy for the door system includes:

[0124] An improved version of the NSGA-II algorithm, which improves population generation and crowding distance calculation, obtains a genetically modified NSGA-II algorithm by selecting the chromosome with the best fitness. This genetically modified NSGA-II algorithm includes the following processing steps:

[0125] A population of PopSize is randomly generated as the initial population. The fitness value of each individual is calculated. The individual with the highest fitness value is found and moved to the parent population IP. When IP = PopSize, a population with inheritance is formed.

[0126] Dynamic congestion distance is used to sort congestion distances using the Euclidean distance product. The congestion distance is calculated as follows:

[0127]

[0128] Among them The Euclidean distance between the j-th solution and its nearest neighbor i, and the steps of the dynamic congestion distance environment selection strategy are as follows:

[0129] Step 1. Merge the non-dominated solutions in the population and let the size be DP1;

[0130] Step 2. Determine the size of individuals in DP1. If DP1 ≥ PopSize, proceed to Step 3; otherwise, proceed to Step 4.

[0131] Step 3. Calculate the Euclidean distance between solutions in DP1, delete the solution with the smallest crowding distance, and make the solution with the smallest crowding distance satisfy DP1 = PopSize;

[0132] Step 4: Calculate the Euclidean distance between the deleted solutions, delete the solution with the smallest crowding distance, and make the number of remaining solutions in DP1 plus the size of the solution equal to PopSize;

[0133] The i-NSGA-II-DC solves a set of non-dominated Pareto optimal solutions in an m-objective optimization problem containing K+1 Pareto optimal solutions, with the membership function δ... i (fk i The expression ) represents the optimality of the i-th objective function in the k-th solution, defined as follows:

[0134]

[0135] Where f I i and f N i Let f represent the lower and upper bounds of the i-th objective function, respectively; k i It is the i-th objective value of the k-th Pareto solution;

[0136] Membership degree η of the solution s Calculate using the following formula:

[0137]

[0138] Where ω i Is the i-th objective satisfying Σω i The weight coefficient is 1, and the membership degree η of all solutions is compared. s The solution corresponding to the maximum membership degree is selected as the optimal preference solution to obtain the optimal maintenance strategy for the door system. The optimal maintenance strategy includes the maintenance cycle T of low-level preventive maintenance, the number of times Np and Nr of low-level preventive maintenance are performed in each high-level preventive maintenance cycle, and the replacement of the parts.

[0139] As can be seen from the technical solutions provided by the embodiments of the present invention described above, the present invention constructs the state transition matrix of the component by analyzing the changes of the component in various states; furthermore, by analyzing the logical structure relationship of the system and using a general generating function to establish the system's performance function, the reliability of the system can be analyzed; and maintenance strategy optimization is performed with the minimum cost rate and maximum output performance as dual objectives.

[0140] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and will become apparent from the description or may be learned by practice of the invention. Attached Figure Description

[0141] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0142] Figure 1 A flowchart illustrating a method for reliability assessment and maintenance strategy optimization of a vehicle door system based on pH distribution, provided in an embodiment of the present invention;

[0143] Figure 2 This is a schematic diagram illustrating the state transition process of a component of a vehicle door system, provided in an embodiment of the present invention.

[0144] Figure 3 This is a schematic diagram of the state change curves of a component of a vehicle door system provided in an embodiment of the present invention;

[0145] Figure 4 A schematic diagram of a vehicle door layout provided for an embodiment of the present invention;

[0146] Figure 5 This is a schematic diagram of a vehicle door system structure provided in an embodiment of the present invention;

[0147] Figure 6 A logic structure block diagram of a vehicle door system provided in an embodiment of the present invention;

[0148] Figure 7 A reliability structure diagram of a vehicle door system provided in an embodiment of the present invention;

[0149] Figure 8 This is a schematic diagram illustrating the performance change of a vehicle door subsystem over time, provided as an embodiment of the present invention.

[0150] Figure 9 This is a schematic diagram illustrating the expected performance of a train door system over time, provided as an embodiment of the present invention.

[0151] Figure 10 A schematic diagram of a Pareto front set provided in an embodiment of the present invention;

[0152] Figure 11 A schematic diagram of the Pareto front of a maintenance strategy provided in an embodiment of the present invention. Detailed Implementation

[0153] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0154] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or couplings. The term “and / or” as used herein includes any and all combinations of one or more of the associated listed items.

[0155] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0156] To facilitate understanding of the embodiments of the present invention, the following will provide further explanation and description with reference to the accompanying drawings and several specific embodiments. These embodiments do not constitute a limitation on the embodiments of the present invention.

[0157] To ensure the safety and reliability of vehicle door systems and avoid delays and downtime due to malfunctions, the maintenance strategy of the system needs to be optimized. This invention proposes a dual-objective maintenance strategy optimization method based on pH distribution and considering multiple maintenance measures. This method obtains the maintenance interval and number of maintenance operations for multi-level preventative maintenance of vehicle doors. For the complex, multi-state system of vehicle doors, a maintenance strategy that meets actual needs is specified based on its reliability changes, providing support for vehicle maintenance.

[0158] A schematic diagram of the processing flow of a door system reliability assessment and maintenance strategy optimization method based on pH distribution provided in this embodiment of the invention is shown below. Figure 1 As shown, the processing steps include the following:

[0159] Step S1: Obtain fault data recorded by the vehicle repair department. Assuming that the dwell time of the component in different states follows a PH distribution, use the deterministic annealing Expectation-Maximization (DAEM) algorithm to estimate the PH distribution parameters.

[0160] Based on the fault data recorded by the vehicle repair department, the fault data is classified and statistically analyzed according to different components. Based on the status of the components, the dwell time of each component in different states is calculated, and the DAEM algorithm is used to estimate the PH distribution parameters.

[0161] The pH distribution is crucial for current research because it can fit any non-negative distribution to a continuous distribution, making system analysis more flexible and better reflective of real-world systems. The pH distribution is represented by a matrix, thus offering greater computational power. In studies estimating the reliability of components / equipment, it's often assumed that the components / equipment follow a certain distribution, which can reduce the accuracy of analytical models to some extent. The pH distribution, however, can effectively approximate any distribution on the non-negative real number axis, offering strong versatility. For vehicle door systems, this invention assumes that the dwell time of components in different states follows a pH distribution by analyzing system reliability and optimizing maintenance strategies. By analyzing vehicle fault repair records from vehicle repair departments, component states are categorized based on fault conditions, yielding the dwell time of components in each state, thus obtaining the observed fault dataset D.

[0162] Here, the PH distribution is the time distribution of the Markov process before it enters the absorption state m+1 in the state space {1,2,…,m,m+1}, denoted as PH(τ,T), (τ,τ) m+1 Let τ = (τ1, τ2, ..., τn) be the initial probability vector of the Markov process. m ), satisfying τ+τ m+1 =1. The infinitesimal generator of this process is:

[0163]

[0164] T is the state transition rate matrix, a non-singular m-order square matrix. It satisfies Te+T 0 =0,T 0 It represents the transition probability from any state to the absorption state m+1. Its probability density function f(·) and cumulative distribution function F(·) are:

[0165] f(x)=τexp(Tx)T 0 x≥0 (2)

[0166] F(x)=1-τexp(Tx)e,x≥0 (3)

[0167] T and T in the distribution 0 These correspond to the generation matrix between transient states and the transition rate vector from the transient state to the absorption state, respectively. Specifically, they are represented as follows:

[0168]

[0169] T 0=(ξ1 ξ2…ξ) m ) T (5)

[0170] D is the observed fault dataset recorded by the vehicle repair department. The observed fault dataset D consists of K samples that satisfy the PH distribution, D=(t1,…,t k Without loss of generality, assume 0. <t1<...<t k Consider an m-order PH distribution in the observed fault dataset D.

[0171] According to the traditional EM algorithm, the unobserved statistic (random variable) is defined as follows:

[0172] Indicator random variable, indicating that the state of the k-th sample starts from order i;

[0173] The dwell time of the kth sample in the i-th state;

[0174] The kth sample t k The number of phase transitions from state i to state j;

[0175] Y i [k] : Indicator random variable, representing the phase i observed in the k-th sample. The likelihood estimation function can be expressed as:

[0176]

[0177] in, θ=(τ1,...,μ 1,2 The elements in θ (ξ1, ..., ξ2, ...) represent the parameter values ​​that need to be estimated for the pH distribution. Introducing the inversion factor, the temporary parameter value θ' of θ is obtained using the following formula.

[0178]

[0179] In the formula v β It is a constant.

[0180] The thermodynamic free energy function estimated by the pH distribution parameters is:

[0181]

[0182] in It is the maximum likelihood estimation function of the PH distribution.

[0183] Based on the transformed parameters, execute the E-step of the DAEM algorithm. (Introduction) and Represented as:

[0184]

[0185] in The random variable representing the pH transition. Since this is a process of pH distribution transformation, the two can be represented as:

[0186]

[0187] For the thermodynamic free energy function F β After minimizing (θ), and introducing transformation parameters, the expected correlation of the fitting parameters for the PH distribution data is:

[0188]

[0189] Then, by performing M steps, the parameter estimates of the PH distribution are obtained as follows:

[0190]

[0191] Where T is a random variable with a PH distribution, and θ' is a temporary parameter vector. Given initial values ​​for β and θ, the temporary parameters of θ are obtained through equation (7). Then, calculate the updated θ value according to the E-step and M-step of the above steps. Increase the β value and repeat the iteration of θ value until β = 1. Calculate the expected value of the unobserved variable using equation (11), and then calculate the estimated PH distribution parameter value τ according to equation (12). i μ i，j and ξ i .

[0192] Step S2: Construct the state transition matrix of the components in the door system based on the PH distribution parameters.

[0193] This invention assumes that the dwell time of a component in each state and the time required for different repairs follow a pH distribution. Based on the statistics of component failure data and repair time, the parameters of each pH distribution can be fitted using the above steps. After obtaining the pH distribution, the following steps are performed.

[0194] Based on the device's state transition process, the device's macro states are defined as follows: The components are assigned a state set S = {1, 2, ..., n, n+1} based on their actual states. The states in set S are categorized into three types according to the component's operational state:

[0195] (1) Healthy state, state set G = {1,2,...,k}, at which time the component is operating well and performing its function.

[0196] (2) Sub-healthy state, where the state set B = {k+1,k+2,...,n} represents components that can perform their functions but are prone to minor malfunctions.

[0197] (3) Maintenance status, the status is set to F={n+1}, which is the status of the component being maintained.

[0198] Assume that the dwell time of components in states G and B follows a PH distribution, denoted as PH(α,T) and PH(β,V), respectively. As the system operates, its performance gradually declines, and the system state transitions from state G to state B. Without maintenance, the system cannot recover from a sub-healthy state to a healthy state. The system's corrective maintenance time follows PH(γ1,L1), low-level preventive maintenance time follows PH(γ2,L2), high-level preventive maintenance time follows PH(γ3,L3), and replacement maintenance time follows PH(δ,M).

[0199] Two levels of preventative and corrective maintenance are performed on components. Lower-level preventative maintenance primarily checks the system's essential functions and surface damage, and cleans the system. Higher-level preventative maintenance involves disassembling and inspecting the system, replacing easily damaged components. System faults discovered during operation or preventative maintenance require timely repair and restoration. For management purposes, both levels of preventative maintenance are performed periodically, with higher-level preventative maintenance following multiple lower-level preventative maintenance sessions. During multiple preventative maintenance sessions, components are replaced or returned to the factory for maintenance to restore their performance to that of new components. Component faults are discovered during maintenance or system malfunctions, without considering hidden faults. Lower-level preventative maintenance does not change the overall state of the system. Higher-level preventative maintenance improves the system's state, restoring equipment to a healthy condition. Corrective maintenance eliminates faults without altering the component's state transition rate. With increasing usage time, component performance gradually decreases, and the component degradation rate increases with aging. Introducing a degradation factor ρ, the pH distribution of the component's residence time in state G and state B is PH(α,ρ). h T) and (β,ρ) h V). Generally speaking, as the service life of a component increases, the time the component spends in each state decreases, so we take ρ>1. If ρ=1, it means that the degradation rate of the component remains unchanged.

[0200] Group the states of the system into macro - states. Let Ω denote the component state space, then Ω = {Α, Γ, Ε, Η, Λ, Ψ}. The macro - states in the state space Ω respectively correspond to the healthy state, sub - healthy state, corrective maintenance state, low - level preventive maintenance state, high - level preventive maintenance state, and replacement state of the component. For discussion, we define {(h, l, i1, i2, c1, c2, c3, ε): 1 ≤ l < Np, 1 ≤ h < Nr, 1 ≤ i1 ≤ m1, 1 ≤ i2 ≤ m2, 1 ≤ c1 ≤ u1, 1 ≤ c2 ≤ u2, 1 ≤ c3 ≤ u3, 1 ≤ ε ≤ w}, where h and l are the number of low - level and high - level preventive maintenance operations performed on the component. i1 and i2 represent the healthy state and sub - healthy state.

[0201] c1, c2, c3, and ε respectively represent the stages of the component in the corrective maintenance, low - level preventive maintenance, high - level preventive maintenance, and replacement states. The phases of these macro - states satisfy:

[0202] Α = {(h, l, i): 1 ≤ l ≤ Np, 1 ≤ h < Nr, 1 ≤ i1 ≤ m1},

[0203] Γ = {(h, l, i): 1 ≤ l ≤ Np, 1 ≤ h < Nr, 1 ≤ i2 ≤ m2},

[0204] Ε = {(h, l, i, c1): 1 ≤ l ≤ Np, 1 ≤ h < Nr, 1 ≤ i2 ≤ m2, 1 ≤ c1 ≤ u1},

[0205] Η = {(h, l, i, c2): 1 ≤ l < Np, 1 ≤ h < Nr, 1 ≤ c2 ≤ u2},

[0206] Λ = {(h, l, i, c3): l = Np, 1 ≤ h < Nr, 1 ≤ c3 ≤ u3},

[0207] Ψ = {(h, l, i, ε): l = Np, h = Nr, 1 ≤ ε ≤ w}.

[0208] Construct the infinitesimal generator matrix according to the state - transition process of the component.

[0209] (1) The state - transition matrix of the component in the working state is denoted as Θ1. It respectively includes the internal transition of the healthy state, the sub - healthy state transition, and the transition from the healthy state to the sub - healthy state.

[0210]

[0211] In the formula, p ΑX represents the probability of transitioning from the macro - state Α to any macro - state X. The transition probabilities from the macro - state Α to the macro - states Γ, Ε, Η, and Λ satisfy p ΑΓ + p ΑΕ + p ΑΗ+p ΑΛ =1. Similarly, for macrostate Γ, the transition probabilities to other macrostates E, H, and Λ satisfy p. ΓΕ +p ΓΗ +p ΓΛ =1.

[0212] The PH distribution is a Markov process defined in the state space, where the change in the probability vector p of a component in a healthy state satisfies:

[0213]

[0214] The probability of transitioning from a healthy state to an initial state is α. The probability of transitioning from a healthy state to a preventative maintenance state at time t is ∑p i (t), p i It is an element of p(t). Two levels of preventative maintenance cannot occur simultaneously, when p ΑΗ or p ΑΛ When determined, the other value is 0. p at time t ΑΕ λ(1-∑p) i (t)), p ΑΓ For (1-λ)(1-∑p) i (t)), where λ is the probability that a healthy state is absorbed and transitions to a faulty state. Similarly, the transition of a component from a sub-healthy state satisfies dp(t) / dt=p(t)V, with an initial state probability of β, p ΓH or p ΓΛ For ∑p i (t), p ΓΕ 1-∑p i (t).

[0215] (2) The state transition matrix from healthy state and sub-healthy state to low-level preventive maintenance state is denoted as matrix Θ2.

[0216]

[0217] (3) The state transition matrix of the component from healthy state and sub-healthy state to corrective maintenance state is Θ3.

[0218]

[0219] (4) The state transition matrix for components that have completed low-level preventive maintenance and whose performance has improved to a healthy state and a sub-healthy state is Θ4.

[0220]

[0221] The initial probabilities of a component completing l low-level preventive maintenance and entering the l+1 low-level preventive maintenance interval are denoted as α(l) and β(l), respectively. Equation (14) calculates the probability of a change in health status at time t. The element value of α(l) is p. i / ∑p i Similarly, β(l) can be derived.

[0222] (5) The component transfer matrix Θ5 in the low-level preventive maintenance state is as follows.

[0223]

[0224] (6) The state transition matrix from the corrective maintenance state to the healthy state and the sub-healthy state is represented by the matrix Θ6.

[0225]

[0226] (7) The state transition matrix within the corrective maintenance state is:

[0227] Based on the transmission process of the component between macro states, the infinitesimal generation matrix Q(h) of the component in the h-th advanced preventive maintenance interval is obtained.

[0228]

[0229] In the formula, lX represents the macro state X of the component after l low-level preventive maintenance. In addition, macro state A and Γ both represent the component in the working state, which is represented by W.

[0230] (8) The state transition matrix of the component from the working state to the advanced preventive maintenance state is Θ7.

[0231]

[0232] (9) After advanced preventive maintenance, the component is transferred to a healthy state, and the state transition matrix is ​​Θ8.

[0233]

[0234] (10) The internal state transition matrix of the component in advanced preventive maintenance state is as follows:

[0235] (11) After the component has undergone Nr-level advanced preventive maintenance, or after the component has been replaced or returned to the factory, the state transition matrix is ​​Θ9.

[0236]

[0237] (12) The transition matrix of the component during the replacement and maintenance state is as follows: After replacement, the component is in a new state, and the transition matrix to the healthy state is M. 0 α.

[0238] In the above process, Θ1-Θ9 are the state transition matrices of two adjacent states that may occur in the operation of the components in the door system. Through matrices Θ1-Θ9, the complete state transition matrix Q of the component is obtained.

[0239] Consider the infinitesimal generation matrix Q of the advanced preventative maintenance component:

[0240]

[0241] The general generating function q of the component at time t is expressed as:

[0242]

[0243] Where p jq (t) represents the component at time t with performance g. q The probability of (j).

[0244] Component q obeys PH(ζ) in every macroscopic state q Q q The initial probability is ζ. q =(α q Let v = 0,0,…,0). jq Indicates the performance of component q in each phase. q (j), p jq (t)=v jq (t)e, denoted as

[0245] According to the Chapman-Kolmogorov equation, the probability of the performance level of component q at time t+Δt can be divided into the following probability combinations.

[0246] ④ The performance of component q at time t is g q (j), and the probability that the performance has not changed is (1+Q) q (jj)Δt)v jq (t) T .

[0247] ② Component q is in performance g at time t. q (b) The performance transfers to g over time Δt. q The probability of (j) is:

[0248] Therefore:

[0249]

[0250] Q q (bj) is the component from the performance g q (b) Transfer to performance g q The transition probability matrix of (j) is expressed as:

[0251]

[0252] When the initial condition is v q (0)=ζ q When the solution to the differential equation is:

[0253] v q (t)=ζ q exp(Q q t) (28)

[0254] For a complex system with N components, the z-transform of the system is denoted as:

[0255]

[0256] Where U(z) is the system function f(u1(z,t),u2(z,t),…,u N (z,t)); g s p are the possible state values ​​of f(·); s Let f(·) be the probability corresponding to f(·). After obtaining the general generating function of the system, the system has M. sys The system's performance states are then used to obtain the system's performance output function.

[0257] Analyze the state processes of components in the train door system. Figure 2 This invention provides a schematic diagram of the state transition process of a component in a train door system. Based on the state transition process of the system component, a state transition matrix of the component is constructed according to equation (20), resulting in a schematic diagram of the component's state change curves, as shown below. Figure 3 As shown.

[0258] Based on historical data of door repair time, the pH distribution under different maintenance conditions was fitted using the pH distribution parameter fitting method in step S1, as shown in Table 1.

[0259] Table 1 pH distribution of maintenance time

[0260]

[0261] By establishing the state transition matrix of the door system, the general generating functions of each key component of the door system are constructed using the improved general generating function method through equations (26)-(28), and then the general generating function of the door system is constructed through equation (29).

[0262] Step S3: Construct the reliability structure of the door system.

[0263] The structure of a vehicle door system provided in this embodiment of the invention is as follows: Figure 4 As shown, the distribution of a train door system is analyzed. The train consists of 8 carriages, each with 4 passenger doors, for a total of 32 doors. Figure 4 As shown, M represents a motor vehicle and T represents a trailer. Passenger doors are controlled by DCUs (Drive Control Units). Each car has one main door control unit (MDCU), and the rest are local door control units (LDCUs). The DCUs of each door in each car are connected via a CAN bus. Inside each car, the MDCU transmits the door status information of each car to the Multifunction Vehicle Bus (MVB), and then forwards the door information of each car to the central control unit, realizing the data exchange of communication information between the train doors.

[0264] The opening and closing of a door requires close cooperation between its components. Door signals are transmitted to the DCU (Distributed Control Unit) of each door. The DCU controls the solenoid valves to open or lock the main and auxiliary locks. Upon receiving the signal, the DCU controls the drive motor to rotate forward and backward, achieving the opening and closing action. During the opening process, when the door button is pressed, a door request is sent to the DCU via the door control circuit. The DCU then commands the solenoid valve to release the latch, simultaneously triggering the main lock position switch contact to send a signal to the DCU. At this time, the DCU sends a signal to release the auxiliary lock position switch. When the opening conditions are met, the DCU energizes the motor, causing the screw to rotate, which in turn opens the door via the support frame. The closing process is roughly the reverse of the opening process. The flowchart of the door system's opening and closing action is shown below. Figure 6 As shown.

[0265] For the door system, components are considered to be connected in series. The operation of each component is controlled by the DCU. Each MDCU controls the door system and transmits signals from other LDCUs. MDCUs are connected in parallel and controlled by the operator's compartment or Automatic Train Operation (ATO). The train door system is a typical complex multi-state system. The structural reliability block diagram of the door system is shown below. Figure 7 As shown in Table 2.

[0266] Table 2 Composition of the door system

[0267]

[0268] Step S4: Obtain the performance output function of the door system based on the state transition matrix of the door component and the reliability structure of the door system.

[0269] A general generating function is constructed for each component in the vehicle door system, defining the performance levels of three component states (healthy state, sub-healthy state, and maintenance state) as 1, 0.5, and 0, respectively. As shown in Table 2, these components belong to the subsystems of the electronic control unit, drive guidance device, and locking device. For a subsystem, if more than half of its components are in a sub-healthy state, the subsystem is considered to be in a sub-healthy state; if any of its components are in a maintenance state, it is considered to be in a maintenance state. Based on the performance changes of each component, the performance change of a vehicle door subsystem over time provided by this embodiment of the invention is as follows: Figure 8 As shown.

[0270] According to the general generation function of the door system, if all three subsystems are in a healthy state, the system is considered to be in a healthy state, and its performance is recorded as 1. If any subsystem is in a sub-healthy state, the door system is considered to be in a sub-healthy state, and its performance is recorded as 0.5. When the system is in maintenance mode, its performance is represented as 0. Figure 4 As shown, the distribution of a train door system is analyzed. A train consists of 8 carriages, each with 4 passenger doors, for a total of 32 doors. This invention studies the door system of a train, where the expected performance of the train is the expected output performance of the 32-door system. The expected performance of a train door system provided by this invention varies over time as follows: Figure 9 As shown.

[0271] Step S5: Establish an optimization objective function for the maintenance strategy of the door system, aiming to minimize the maintenance cost rate and maximize the expected output performance. Solve the objective function using the NSGA-II algorithm based on dynamic congestion distance to obtain the optimal maintenance strategy for the door system.

[0272] The two objectives of this invention are to maximize desired performance and minimize cost. The cost of each corrective maintenance is M. cf The cost of basic preventive maintenance is M. cl The cost of advanced preventive maintenance is M. ca The cost of replacement and repair is M. cr Where p w (t) and p f (t) represent the probabilities of the system being in an operating state and a maintenance state, respectively. The objective function for optimizing the maintenance strategy is as follows:

[0273]

[0274]

[0275] st

[0276]

[0277] By deriving the above steps step by step, the general generating function of the system performance in equation (29) is obtained. From the constructed general generating function, the probability of the system being in each performance state at time t can be obtained. w (t) and p f (t) represents the probability of the system being in an operating state and a maintenance state, which can be obtained from this general generating function. By obtaining the probability values ​​of the system in each state, the output performance and maintenance cost of the system are calculated. Under the condition of satisfying constraints, the output performance is maximized and the maintenance cost is minimized, thereby optimizing the maintenance cycle and the number of maintenance operations.

[0278] Equation (30) indicates that the first objective function of the model is to maximize the expected performance output, and the system performance and probability are given by Equation (29). Equation (31) is the second objective function, which minimizes the maintenance cost rate. Equation (32) is the reliability constraint, R. l This represents the lower limit of system reliability.

[0279] The objectives of this invention are to minimize the maintenance cost rate and maximize the expected output performance, optimized using an improved NSGA-II algorithm. To obtain a high-quality population and maintain population diversity, a non-dominated sorting genetic algorithm based on genetics and dynamic crowding distance (NSGA-II-DC) is proposed, improving the population generation and crowding distance calculation in the NSGA-II algorithm. By selecting chromosomes with optimal fitness, a high-quality population is formed, improving the search speed of the algorithm; this is called genetically-enabled NSGA-II (i-NSGA-II). Furthermore, NSGA-II utilizes crowding distance to maintain population diversity. Non-dominated solutions are sorted by calculating crowding distance, and solutions with small crowding distances are removed. However, this method does not consider the change in crowding distance between the remaining solutions when a solution is removed. We propose an NSGA-II algorithm based on dynamic crowding distance (NSGA-II-DC). The dynamic crowding distance environment selection strategy calculates and sorts the individual crowding distances, deletes the solution with the smallest crowding distance, recalculates the crowding distances between the remaining solutions, updates and deletes the solution with the smallest crowding distance again, and repeats this process until the population size meets the requirements. Therefore, i-NSGA-II-DC dynamically discards the worst individuals during the evolutionary process and ensures that the solution set is as sparse as possible, thereby obtaining the Pareto front solution set.

[0280] A flowchart of an i-NSGA-II-DC algorithm provided in this embodiment of the invention is as follows: Figure 10 As shown, the processing steps include the following:

[0281] A population of size PopSize is randomly generated as the initial population. The fitness value of each individual is calculated, and the individual with the highest fitness value is moved to the parent population IP. When IP = PopSize, a population with inheritance is formed.

[0282] Dynamic congestion distance sorting, utilizing the Euclidean distance product, can reduce computational complexity and increase solution diversity. The congestion distance is calculated as follows:

[0283]

[0284] Among them The Euclidean distance between the j-th solution and its nearest neighbor solution i. The main steps of the dynamic congestion distance environment selection strategy are as follows.

[0285] Step 1. Merge the non-dominated solutions in the population and let the size be DP1.

[0286] Step 2. Determine the size of individuals in DP1. If DP1 ≥ PopSize, proceed to Step 3; otherwise, proceed to Step 4.

[0287] Step 3. Calculate the Euclidean distance between solutions in DP1, and remove the solution with the smallest crowding distance to satisfy DP1 =

[0288] PopSize.

[0289] Step 4: Calculate the Euclidean distance between the deleted solutions, delete the solution with the smallest crowding distance, and make the number of remaining solutions in DP1 plus the size of the solution equal to PopSize.

[0290] The selection process here employs a tournament selection method. A certain number of individuals are randomly selected from the parents, and the individuals with the highest fitness are selected for genetic processing until the offspring population is the same size as the parent population. In this way, population diversity is largely preserved.

[0291] Crossover is used because gene coding is simple, employing a single-point crossover. If the random number is less than the crossover coefficient Pc, two chromosomes are selected as parents, and a gene segment from one of them is chosen for crossover to produce two new chromosomes as offspring.

[0292] The mutation operation is a single-point mutation. When the random number is less than the coefficient of variation Pm, a gene segment of the parent chromosome is selected and altered to become the chromosome of the new offspring.

[0293] The i-NSGA-II-DC algorithm solves a set of non-dominated Pareto optimal solutions, but decision-makers need to select the optimal solution based on actual requirements. In an m-objective optimization problem containing K+1 Pareto optimal solutions, the membership function δ... i (f k i Let represent the optimality of the i-th objective function in the k-th solution. Its definition is as follows:

[0294]

[0295] Where f I i and f N i Let f represent the lower and upper bounds of the i-th objective function, respectively; k i It is the i-th objective value of the k-th Pareto solution.

[0296] Membership degree η of the solution s Calculate using the following formula:

[0297]

[0298] Where ω i Is the i-th objective satisfying Σω i The weight coefficient is 1, and its value is determined by the decision-maker's preferences. Compare the membership degrees η of all solutions. s The solution with the highest membership degree is selected as the optimal preferred solution. The optimal maintenance strategy for the door system is obtained, which includes a low-level preventive maintenance cycle T, the number of low-level preventive maintenance operations Np and the number of high-level preventive maintenance operations Nr within each high-level preventive maintenance cycle, followed by component replacement.

[0299] In this invention, the two objectives are to minimize the cost rate and maximize the expected performance. The i-NSGA-Ⅱ-DC algorithm is used for solving this problem, and the algorithm parameters are set as shown in Table 3. The reliability lower limit is set to 0.9, and the maintenance costs for fault repair, low-level preventive maintenance, high-level preventive maintenance, and replacement maintenance are 24200, 15400, 48200, and 704000 yuan, respectively.

[0300] Table 3i-NSGA-Ⅱ-DC Parameter Settings

[0301]

[0302] The Pareto front set obtained as the optimal solution is as follows: Figure 11 As shown. From Figure 11 As can be seen, reducing costs and maintaining good performance are contradictory. A considerable investment is required to ensure the system's high-performance output.

[0303] With the weights of these two objectives set to 0.5, the optimal maintenance strategy solution, obtained using fuzzy logic decision-making, yielded T=55, Np=11, Nr=4, and the optimal membership degree was 0.9137. Table 4 shows the comparison between the optimized maintenance strategy and the railway company's existing maintenance strategy. It is evident that the optimized maintenance strategy extends the time interval for low-level maintenance and reduces the number of maintenance events. This results in a 7.11% reduction in the system's maintenance cost rate, while the system's output performance remains almost unchanged, decreasing by only 0.45%. Furthermore, the optimized strategy extends the system's lifespan, making maintenance more efficient and economical.

[0304] Table 4 Comparison of Maintenance Strategies

[0305]

[0306] In summary, due to the versatility of the pH distribution, the state transition matrix of the system constructed based on the pH distribution more realistically describes the system. The reliability function constructed by this invention is based on the system's logical structure, providing a more accurate characterization of system performance. Furthermore, this invention considers both minimum maintenance cost rate and maximum expected output performance, better aligning with actual maintenance goals, and the resulting maintenance solution better meets practical needs. The pH distribution offers advantages such as good computational efficiency and ease of analysis, making it more convenient to operate and providing reference and theoretical support for actual vehicle system maintenance.

[0307] This invention addresses the complex, multi-state system of vehicle door systems. Based on actual maintenance needs, it considers various maintenance measures including two-level preventative maintenance, component replacement, and fault repair, providing a reference for practical maintenance strategies. It analyzes the state changes of components during service and constructs a state transition matrix for the components based on the pH distribution.

[0308] This invention constructs a state transition matrix for components by analyzing their changes in various states. Furthermore, by analyzing the logical structure of the system and utilizing a general generating function, it establishes the system's performance function, enabling the analysis of system reliability. Maintenance strategy optimization is then performed with the dual objectives of minimizing cost and maximizing output performance. This method incorporates the pH distribution, leveraging its properties to enhance the flexibility, versatility, and computational efficiency of the model construction. Moreover, this invention provides more accurate system analysis compared to traditional methods. The proposed maintenance strategy better aligns with actual maintenance needs, and the dual-objective optimization meets the expectations of managers regarding maintenance outcomes. Therefore, this invention not only offers economic benefits but also social benefits.

[0309] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of one embodiment, and the modules or processes shown in the drawings are not necessarily essential for implementing the present invention.

[0310] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that the present invention can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of the present invention.

[0311] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for apparatus or system embodiments, since they are basically similar to method embodiments, the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. The apparatus and system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0312] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A PH distribution-based reliability evaluation and repair strategy optimization method for a vehicle door system, characterized by, include: Fault data recorded by the vehicle repair department is obtained. Assuming that the dwell time of components in the door system in different states follows a PH distribution, the deterministic annealing expectation-maximization (DAEM) algorithm is used to estimate the PH distribution parameters. Based on the PH distribution parameters, the state set of the components in the door system is obtained, the state transition matrix of the components in the door system is constructed, and the general generating function of the door system is generated based on the state transition matrix of the components in the door system. Construct a reliability structure for the vehicle door system, obtain the performance output function of the vehicle door system based on the general generation function and reliability structure of the vehicle door components, and obtain the output performance and maintenance cost of the vehicle door system based on the performance output function of the vehicle door system. With the goals of minimizing maintenance cost rate and maximizing expected output performance, an optimization objective function for the maintenance strategy of the door system is established. The optimization objective function is solved using the NSGA-II algorithm based on dynamic congestion distance to obtain the optimal maintenance strategy for the door system. The acquisition of fault data recorded by the vehicle repair department assumes that the dwell time of components in the door system under different states follows a PH distribution. The DAEM algorithm is used to estimate the PH distribution parameters, including: According to the fault data recorded by the vehicle maintenance department, the fault data is classified and counted according to different components, the residence time of each component in different states is counted according to the state of the component, it is assumed that the residence time of the component in different states obeys the PH distribution, the DAEM algorithm is adopted for PH distribution parameter estimation, the residence time of the component in each state is obtained, and an observation fault data set is constructed D ; PH distribution is the time distribution of the Markov process in the state space {1, 2, …, m, m+1} before entering the absorbing state m+1, denoted as PH τ , T ), ( τ , τ m+1 ) is the initial probability vector of the Markov process, τ = ( τ 1, τ 2, …, τ m ), satisfying τ + τ m+1 =1, and the infinitesimal generator of this process is: T is the transition rate matrix between states, is a non-singular m x m matrix satisfying Te T 0 = 0, T 0 is the transition probability from any state to the absorbing state m+1, the probability density function f and the cumulative distribution function F are given by:​​​ In distribution and The production matrix and the transition rate vector from the transient state to the absorption state, respectively, are represented as follows: D A dataset of observed faults recorded by the vehicle repair department. D Depend on K The sample consists of a pH distribution, D=( t 1,…, t k ), assuming 0 < t 1< ...< t k Consider the observed fault dataset D Obedience m pH distribution; According to the EM algorithm, the unobserved statistic is defined as follows: : Indicator random variable, representing the first k The state of each sample is from i Step begins; : No. k The sample is in the first... i The duration of the state; : No. k Sample t k From i State transition j The number of phase transitions in the state; : Indicator random variable, representing the first k The phase observed for each sample is i The likelihood estimation function can be expressed as: Where Z=( , , ), , θ The elements in the equation represent the parameters that need to be estimated for the pH distribution. Introducing the inversion factor, the following formula is used to obtain the values. θ Temporary parameter values θ '; In the formula v β It is a constant; The thermodynamic free energy function estimated by the pH distribution parameters is: in It is the maximum likelihood estimation function of the PH distribution; Based on the transformed parameters, the E-step of the DAEM algorithm is executed, introducing... and , is represented as: in The random variable representing the pH transition. The pH distribution transformation process can be represented as follows: With respect to the thermodynamic free energy function F β ( θ After minimization, introducing transformation parameters, the expected correlation of the fitting parameters for the PH distribution data is: Then, by performing M steps, the parameter estimates of the PH distribution are obtained as follows: in T Let be a random variable with a PH distribution. θ' Given a temporary parameter vector. β and θ The initial values ​​of the parameters are obtained through equation (7). θ Temporary parameters Calculate the updated values ​​based on steps E and M above. θ Value, increase β Values ​​and iterate continuously. θ Value until β =1, calculate the expected value of the unobserved variable using equation (11), and then calculate the estimated PH distribution parameter value according to equation (12). , and .

2. The method according to claim 1, characterized in that, The method of obtaining the state set of components in the door system based on the PH distribution parameters and constructing the state transition matrix of the components in the door system includes: Determine the state set of the component based on its actual state. S ={1, 2,…, n , n +1}, set S The status of the components is divided into three categories based on their operational status: (1) Healthy state, state set G={1, 2, ..., k }; (2) Sub-health state, where the state set B = { k +1, k +2, ..., n }; (3) Maintenance status, the status is set to F={ n +1}; Assuming the component is in state G and B The residence times follow a pH distribution, denoted as pH( α , T ) and PH( β , V The system state changes from state 1 to 2. G Transition to state B The system's corrective repair time follows PH( γ 1, L 1) The time for basic preventive maintenance follows the PH ( ) rule. γ 2, L 2) Advanced preventive maintenance time conforms to pH ( γ 3, L 3) The replacement and repair time follows PH( δ , M ); Introducing degradation factors ρ The pH distributions of the component's residence time in state G and state B are respectively PH ( α , ρ h T ) and( β , ρ h V ),Pick ρ >1, group the system's states into macroscopic states, let... Ω To represent the component state space, then Ω = { A , Γ , E , H , Λ , Ψ }, state space Ω The macro states in the code correspond to the component's health status, sub-health status, corrective maintenance status, low-level preventive maintenance status, high-level preventive maintenance status, and replacement status, respectively. The definition is {( h , l , i 1, i 2, c 1, c 2, c 3, ε ): 1 ≤ l < Np ,1 ≤ h < Nr , 1 ≤ i 1≤ m 1, 1 ≤ i 2≤ m 2, 1 ≤ c 1 ≤ u 1, 1≤ c 2 ≤ u 2, 1 ≤ c 3 ≤ u 3, 1 ≤ ε ≤ w },in h , l The number of low-level and high-level preventative maintenance sessions performed on this component. i 1, i 2 indicates healthy state and sub-health state. c 1, c 2, c 3 and ε represent the stages of a component under corrective maintenance, low-level preventive maintenance, high-level preventive maintenance, and replacement conditions, respectively. The phases of these macroscopic states satisfy the following: Based on the state transition process of the component, construct the infinitesimal generator matrix of the component; (1) The state transition matrix of the component in the working state is denoted as: Θ 1. It includes the internal transfer of a healthy state, the transfer of a sub-healthy state, and the transfer from a healthy state to a sub-healthy state; In the formula, p ΑX Indicates from macro state A Transition to any macro state X The probability from the macrostate A To macro state Γ , E , H and Λ The transition probability satisfies p ΑΓ + p ΑΕ + p ΑΗ + p ΑΛ =1, macro state Γ Switch to other macro states E , H and Λ The transition probability satisfies p ΓΕ + p ΓΗ + p ΓΛ =1; The PH distribution is a Markov process defined in the state space, representing the probability vector of a component in a healthy state. p The changes satisfy: The probability of transitioning from a healthy state to an initial state is α , t The probability of transitioning from a healthy state to a preventative maintenance state at any given time is: , p i yes p ( t The elements of ) and two levels of preventive maintenance cannot occur simultaneously, when p ΑΗ or p ΑΛ When determined, the other value is 0. t Moment p ΑΕ for λ (1- ), p ΑΓ For (1- λ (1-) ), where λ is the probability that a healthy state is absorbed and transferred to a faulty state, and the transition of a component from a sub-healthy state satisfies The initial state probability is β , p ΓH or p ΓΛ for , p ΓΕ For 1- ; (2) The state transition matrix from healthy state and sub-healthy state to low-level preventive maintenance state is denoted as matrix. Θ 2; (3) The state transition matrix of the component from healthy state and sub-healthy state to corrective maintenance state is as follows: Θ 3; (4) The state transition matrix for components that have completed basic preventative maintenance and whose performance has improved to a healthy or sub-healthy state is as follows: Θ 4; Component completed l Secondary-level preventive maintenance and entry l The initial probabilities of the +1 low-level preventive maintenance interval are denoted as follows: α ( l )and β ( l Equation (14) is used to calculate... t The probability of changes in health status at any given time. α ( l The element value of ) ; (5) Component transfer matrix during low-level preventive maintenance Θ 5 as follows: (6) The state transition matrix from the corrective maintenance state to the healthy state and the sub-healthy state is represented by the matrix as follows: Θ 6; (7) The state transition matrix within the corrective maintenance state is: ; Based on the transmission process of the element between macro states, the element in the first macro state is obtained. h Infinitesimal generation matrix within a high-level preventive maintenance interval Q ( h ); In the formula lX Indicates that the component has passed l After the lowest level of preventative maintenance, it enters a macro state. X Macro state A and Γ Both indicate that the component is in a working state; the working state is represented by... W express; (8) The state transition matrix of a component from its working state to its advanced preventive maintenance state is as follows: Θ 7; (9) After advanced preventative maintenance, the component transitions to a healthy state, and the state transition matrix is ​​as follows: Θ 8; (10) The internal state transition matrix of the component in advanced preventive maintenance state is as follows: ; (11) The components have been processed Nr For sub-advanced preventative maintenance, after component replacement or return to the factory, the state transition matrix is ​​as follows: Θ 9; (12) The transition matrix of the component during the replacement and maintenance state is as follows: After replacement, the component is in brand new condition, and the transition matrix for transitioning to a healthy state is as follows: M 0 α ; In the above processing Θ 1—— Θ 9 represents the state transition matrix between two adjacent states that may occur during the operation of a component in the door system. This matrix... Θ 1—— Θ 9. Obtain the complete state transition matrix Q of the component.

3. The method according to claim 2, characterized in that, The general generating function for generating the door system based on the state transition matrix of the components in the door system includes: Consider the infinitesimal generation matrix of advanced preventive maintenance components Q for: General generation function for components q At any moment t Represented as: in p jq ( t ) is the component at time . t In terms of performance g q ( j The probability of ). part q In each macroscopic state, it obeys PH( ζ q , Q q The initial probability is ζ q = ( α q Let (x, y, 0, 0, …, 0) be an integer. v jq Indicates components q Performance in each phase g q ( j ), , recorded as ; According to the Chapman-Kolmogorov equation, components q At any moment t + Δt The probability of performance level can be divided into the following probability combinations: ② Components q At any moment t The performance is g q ( j The probability that the performance remains unchanged is... ; ② Components q At any moment t Always in performance g q ( b Performance over time Δt Transferred to g q ( j The probability of () is: ; Therefore: in Q q ( bj ) is a component based on performance g q ( b ) Shift to performance g q ( j The transition probability matrix of ) is expressed as: When the initial condition is v q (0)= ζ q When the solution to the differential equation is: For those N A complex system of individual components, a system z- The transformation is denoted as: in U ( z ) is a system function of UGF f ( u 1( z , t ), u 2( z , t ), …, u N ( z , t )); g s yes f ( The possible state values ​​of ). p s yes f ( The corresponding probability of ) Based on the state transition matrix of the door system, the general generating functions of each key component of the door system are constructed using the improved general generating function method through equations (26)-(28). The general generating function of the door system is constructed through equation (29). Based on the general generating function of the door system, various performance states of the door system are obtained, and then the performance output function of the door system is obtained.

4. The method according to claim 3, characterized in that, The aforementioned construction of the reliability structure of the vehicle door system, obtaining the performance output function of the vehicle door system based on the general generation function and reliability structure of the vehicle door components, and obtaining the output performance and maintenance cost of the vehicle door system based on the performance output function of the vehicle door system, includes: The train is configured with multiple carriages, each containing multiple passenger doors. M represents a motor vehicle and T represents a trailer. The passenger doors are controlled by door control units. Each carriage has one main door control unit, and the rest are local door control units. Within each carriage, the main door control unit transmits the door status information of each carriage to the multi-function vehicle bus, and then forwards the door information of each carriage to the central control unit, realizing data exchange between the train door communication information. The actions of each component in the door system are controlled by the DCU. Each transport control door system transmits signals from other LDCUs, and the MDCUs are connected in parallel with each other. Construct a general generation function for each component in the door system, and define the performance levels of the healthy state, sub-healthy state, and maintenance state of the component as 1, 0.5, and 0, respectively. Each component in the door system belongs to three subsystems: electronic control unit, drive guidance device, and locking device. For a subsystem, if more than half of the components are in a sub-healthy state, the subsystem is considered to be in a sub-healthy state; if any component is in a maintenance state, it is considered to be in a maintenance state. According to the performance output function of the door system, if all three subsystems are in a healthy state, the system is considered to be in a healthy state and the performance is recorded as 1; if any subsystem is in a sub-healthy state, the door system is considered to be in a sub-healthy state and the performance is recorded as 0.5; when the system is in a maintenance state, the performance is represented as 0.

5. The method according to claim 4, characterized in that, The optimization objective function for establishing a maintenance strategy for the vehicle door system, which aims to minimize the maintenance cost rate and maximize the expected output performance, includes: The optimization objective of the maintenance strategy for the vehicle door system is to maximize expected performance and minimize the cost rate, with the cost of each corrective maintenance being... M cf The cost of basic preventive maintenance is M cl The cost of advanced preventive maintenance is M ca The cost of replacement and repair is M cr , p w ( t )and p f ( t Let and represent the probabilities of the system being in a working state and a maintenance state, respectively. The objective function for optimizing the maintenance strategy of the door system is as follows: p w ( t )and p f ( t ) represents the probability of the system being in a working state and a maintenance state. Equation (30) represents the objective function to maximize the expected performance output. The performance and probability of the door system are given by equation (29). Equation (31) is the objective function to minimize the maintenance cost rate. Equation (32) is the reliability constraint. R l This represents the lower limit of system reliability.

6. The method according to claim 5, characterized in that, The method of using the NSGA-II algorithm based on dynamic congestion distance to solve the optimization objective function and obtain the optimal maintenance strategy for the door system includes: An improved version of the NSGA-II algorithm, which improves population generation and crowding distance calculation, obtains a genetically modified NSGA-II algorithm by selecting the chromosome with the best fitness. This genetically modified NSGA-II algorithm includes the following processing steps: The population size is randomly generated. PopSize Using individuals as the initial population, calculate the fitness value of each individual, find the individual with the highest fitness value, and move the individual with the highest fitness value to the parent population. IP ,when IP = PopSize At that time, a population with inheritance is formed; Dynamic congestion distance is used to sort congestion distances using the Euclidean distance product. The congestion distance is calculated as follows: Among them No. j Each solution and its nearest neighbor solution i The steps for selecting a dynamic congestion distance environment based on Euclidean distance are as follows: Step 1. The size of the non-dominated solutions in the merged population is DP 1; Step 2. Confirm DP The size of the individuals in 1, if DP 1≥ PopSize If yes, proceed to step 3; otherwise, proceed to step 4. Step 3. Calculation DP The Euclidean distance between solutions in step 1 is used to remove the solution with the smallest crowding distance, ensuring that the solution with the smallest crowding distance satisfies... DP 1 = PopSize ; Step 4: Calculate the Euclidean distance between the deleted solutions, and delete the solution with the smallest crowding distance, so that... DP The number of remaining solutions plus the size of the solutions in step 1 is PopSize ; i-NSGA-II-DC solves a set of non-dominated Pareto optimal solutions, including K +1 Pareto optimal solution m In the goal optimization problem, the membership function δ i ( f k i ) indicates the first i The objective function at the th ... K The optimality of a solution is defined as follows: in f I i and f N i They represent the first i Lower and upper bounds of the objective function; f k i It is the first k The Pareto solution of the first... i One target value; Membership degree of the solution η s Calculate using the following formula: in ω i It is the first i The goal satisfies Σ ω i A weight coefficient of 1 is used to compare the membership degrees of all solutions. η s The solution corresponding to the maximum membership degree is selected as the optimal preference solution, thus obtaining the optimal maintenance strategy for the door system. This optimal maintenance strategy includes low-level preventive maintenance cycles. T The number of low-level preventive maintenance operations performed within each high-level preventive maintenance cycle. Np Replace the parts after Nr of advanced preventative maintenance.

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