A reliability assessment and maintenance control method based on time-varying coupling of high-dimensional environmental characteristics

Abstract

This invention provides a reliability assessment and maintenance control method based on time-varying coupling of high-dimensional environmental characteristics. The steps are as follows: Step 1, single-factor environmental effect modeling; Step 2, multi-factor environmental effect coupling; Step 3, reliability modeling and assessment; Step 4, maintenance strategy planning; Step 5, operation and maintenance cost calculation; Step 6, operation and maintenance cost optimization. Through the above steps, this invention realizes the construction of a device reliability assessment model that can adaptively couple multi-source environmental effects, designs a preventive maintenance strategy planning method based on real-time reliability assessment, studies a heuristic algorithm for the operation and maintenance cost model, and obtains a device reliability assessment method and an optimal control strategy planning method under multi-source environmental effects.

Description

Technical Field

[0001] This invention provides a reliability assessment and maintenance control method based on time-varying coupling of high-dimensional environmental characteristics. This method addresses the continuous performance degradation and failure risk of equipment subjected to multi-source environmental effects under dynamic service environments. It introduces environmental covariate parameters, constructs an adaptive equipment reliability assessment model capable of coupling multiple stochastic environmental effects, formulates a maintenance strategy planning method based on real-time reliability assessment, and designs a joint optimization algorithm for inspection cycles and maintenance control. This provides technical support for improving equipment service reliability and reducing failure risk losses. It is applicable to reliability modeling, assessment, and maintenance control decision optimization for equipment whose performance degradation is affected by complex environmental effects. Background Technology

[0002] Large mechanical equipment such as ocean-going ships and aerospace vehicles are subjected to dynamic and varied environmental stresses during their service life, encompassing typical factors such as temperature changes, humidity variations, vibration, and shock. These environmental factors have a significant impact on the equipment's performance degradation process, leading to accelerated cumulative degradation and a significantly increased risk of failure. Traditional reliability modeling and assessment methods often only consider the equipment's own performance degradation process, neglecting the influence of the time-varying characteristics of the service environment on the degradation process. This results in a large deviation between the equipment's reliability assessment and life prediction results and the actual remaining life of the equipment.

[0003] Currently, equipment maintenance planning typically relies on reliability model assessments to develop preventative maintenance strategies based on the equipment's age and performance degradation. When accumulated performance degradation reaches a preset maintenance threshold, downtime maintenance is triggered. However, in actual equipment service, due to the time-varying nature of external environmental factors, static maintenance thresholds can lead to overly conservative or aggressive maintenance strategies, resulting in higher maintenance costs or safety risks.

[0004] To address the risks of equipment performance degradation and failure under the influence of complex time-varying random environmental effects, and to ensure the safety and stability of equipment service, this study focuses on continuously degrading equipment affected by multi-source environmental coupling effects. With the goal of ensuring equipment service efficiency and improving economic benefits, it improves traditional reliability modeling methods and static maintenance strategies, achieves dynamic adaptive coupling of multi-source time-varying environmental effects, constructs a reliability assessment model that considers complex environmental effects, designs a dynamic preventive maintenance strategy based on the improved reliability assessment model, and conducts adaptive joint optimization of degradation state detection intervals and preventive maintenance reliability thresholds. Summary of the Invention

[0005] (1) Purpose of the present invention: The present invention is aimed at continuously degrading equipment affected by multi-source environmental coupling effects. It innovatively constructs a reliability assessment and maintenance control method based on time-varying coupling of high-dimensional environmental characteristics, and designs a dynamic maintenance planning method based on real-time reliability assessment, so as to achieve the goal of ensuring equipment service reliability, reducing equipment downtime losses and maintenance costs.

[0006] (2) Technical solution:

[0007] During equipment service, due to factors such as unstable operating conditions and random measurement errors, the degradation process model exhibits uncertainty. Therefore, stochastic process models are well-suited for degradation modeling. Random variables {X(t), t≥0} are used to represent the cumulative performance degradation during equipment operation. This invention employs a generalized stochastic process to describe equipment degradation, namely… in, The function represents the degradation trajectory affected by multi-source environmental effects, where β is the inherent set of degradation parameters of the device itself, which is not affected by environmental factors; and θ is the set of parameters affected by environmental effects. Let be a random variable with respect to time t, to characterize the random factors in the process. The diffusion parameter is fixed, representing the randomness in the degradation process.

[0008] This invention provides a reliability assessment and maintenance control method for time-varying coupling of high-dimensional environmental characteristics, comprising the following steps: Figure 5 As shown;

[0009] Step 1: Single-factor environmental effect modeling;

[0010] For a single environmental factor, its state can be divided into a finite set of states E = {e1, e2, ..., e}. N}, e i ∈E represents the environmental state, such as temperature falling within a certain range. Within the time interval Δt, the environmental state is determined by e. i ∈E transfer to e j The probability of ∈E can be expressed as P ij (Δt), which has the following properties:

[0011]

[0012] When the time interval approaches 0, i.e., Δt→0, the following limit expression holds:

[0013]

[0014] Among them, P ii (Δt) represents the environmental state e i The probability of staying at time Δt, q ij and qi These represent environmental states e respectively. i To e j The state transition probability density and the environmental state remain at e i The state transition rate. Generally, the state transition probability density of a Markov process is stable, therefore:

[0015]

[0016] Therefore, according to the environmental instantaneous transfer rate matrix According to the Kolmogorov forward equation, for any time interval Δt, the state transition probability matrix is:

[0017] The impact of environmental factors on the degradation process is considered and characterized in the form of an acceleration factor, that is, for a certain parameter θ in the parameter set θ affected by environmental effects. j In environmental state e i Under the influence of ∈E, it has an acceleration factor α ij ,Right now α is the effect matrix of this environmental factor.

[0018] Step 2: Coupling of multiple environmental effects;

[0019] Considering that equipment degradation is affected by K environmental effects, their state sets are respectively E k If 0 < k < K, then the influence effect matrix corresponding to the environmental factors is α. k .

[0020] At a certain time τ, the state probability vector of the k-th environmental factor is P. k,τ The i-th element represents the probability that the environmental factor is in the i-th state at time τ. Due to the time-varying nature of environmental effects, the parameters of the degradation process also have time characteristics. Under the influence of the k-th environmental factor, the parameter set θ affected by the environmental effect is converted into a time-varying parameter set θk. k,τ Under the influence of this environmental factor, θ k,τ The expectation is:

[0021]

[0022] in, Let be the extended matrix of θ, i.e., diag(θ). It satisfies:

[0023]

[0024] Under the influence of environmental effects and multiple environmental factors, the parameter set θ affected by environmental effects is converted into a time-varying parameter set θ. τ . For θτ The extended matrix, i.e., diag(θ) τ The degradation parameter can be expressed as:

[0025]

[0026] Represents the extended matrix diag(P) k,τ α k The expected value of the set of equipment degradation parameters under the combined influence of K environmental effects. Extraction. The diagonal elements can be used to obtain θ τ The expected value E[θ τ ].

[0027] Step 3: Reliability modeling and assessment;

[0028] Equipment degradation is a stochastic process Statement. Taking the initial operating state of the equipment as the cumulative degradation amount of 0, a failure threshold L is set, i.e., X(t) > L. This indicates that the equipment has failed. This indicates that the device, starting from time τ, operates at a fixed parameter θ. τ The probability density distribution of the cumulative degradation amount x within time t.

[0029] First, calculate the state transition probability of the k-th environmental factor experiencing an environmental state of iδ before the next decision point:

[0030]

[0031] in, For 1×m k The vector, m k π represents the number of possible states for the k-th element. k This represents the k-th element in the environmental state Π, that is, the state of the k-th environmental factor. The π k One element is 1, and the rest are 0. Let iδ be the state transition matrix of the k-th environmental factor, which can be obtained from... Calculate. Then, from iδ to (i+1)δ, the expected degradation parameter of the device is:

[0032]

[0033] Extracting the diagonal elements yields the parameter vector E[θ]. τ+iδ |Π].

[0034] Due to the time-varying nature of environmental effects, the parameter set θ exhibits uncertainty over time. Let δ be the minimum time unit for the duration of the environmental effect. Then, at any time τ, the cumulative degradation of the measuring equipment is X. τ The environmental status is Π τ Then its reliability within time ωδ is:

[0035]

[0036] Where, E[θ τ+iδ |Π τ ] indicates the initial environmental state Π τ The expected degradation parameter set at τ+nδ can be derived from equation (6). Then extract the diagonal elements to obtain x. i This represents the amount of degradation at iδ. The probability density distribution of the cumulative degradation of the device at τ+ωδ can also be given as:

[0037]

[0038] Step 4: Maintenance strategy planning;

[0039] Based on the reliability assessment model considering multi-source environmental effects given above, the equipment maintenance strategy is planned as follows:

[0040] (1) Periodic degradation state detection is performed with ωδ as the detection interval, and the detection cost is C. I Degradation status detection can: (a) determine whether equipment has failed; (b) measure the degradation status of equipment;

[0041] (2) If the system is found not to have failed during degradation status detection, one of the following actions may be taken: (a) No maintenance is performed, allowing the equipment to continue in service; (b) Preventative maintenance is performed, and the maintenance costs are borne by the user. P Examples of degradation trajectories resulting from preventative maintenance can be seen. Figure 1 ;

[0042] (3) If a system failure is detected during degradation state detection, corrective repairs must be performed, and the repair costs C must be borne. F And there is C F >C P Examples of degradation trajectories that can be performed through restorative repairs can be seen. Figure 2 ;

[0043] (4) If a failure occurs within the detection interval, downtime costs will be incurred, amounting to C per δ time interval. down .

[0044] Step 5: Calculate maintenance costs;

[0045] At any decision point nωδ, the cumulative degradation state X of the detection equipment is measured. n The current operating environment state Π of the device is obtained. (n, x, Π) constitutes a discrete-time Markov chain, and its transition probability is related to the device age. At the nth detection point, the optimal device operation and maintenance cost is given as:

[0046]

[0047] Among them, C ω (n,x,Π) represents the expected cost of no equipment failure and no preventative maintenance, specifically:

[0048]

[0049] Among them, e -rδ Represents the discount factor; R(·) and g(·) are defined by equations (9) and (10), E[V δ [(n+1,x′,Π′)|Π] represents the expected equipment maintenance cost at the next detection point, given the state of (n+1,x′). k,ω (Π) can represent the state probability of the k-th environmental factor at the next detection point. From equation (9), we can obtain:

[0050]

[0051] in, P represents k,ω (Π)ith k There are elements, m1…m K This represents the number of possible states for each of the first to the Kth environmental factors.

[0052] P ω (n,x,Π) represents the expected cost of performing preventative maintenance when the equipment has not failed, specifically:

[0053] P ω (n,x,Π)=C P +V ω (0,0,Π). (14)

[0054] C F +V ω (0,0,Π) represents the cost that the equipment must bear when it fails at the detection point.

[0055] Step 6: Optimize operation and maintenance costs;

[0056] It can be noted that due to the monotonicity of R(ωδ|nωδ,x,Π) with respect to x, the cost function C ω (n,x,Π) is clearly monotonically increasing with respect to the cumulative degradation x, indicating the existence of a control threshold x.* When (n,Π)<ξ, preventive maintenance is the optimal strategy when the cumulative degradation exceeds this threshold.

[0057] Because calculating the cost function is too complex, this invention develops a value iterative optimization algorithm. This algorithm can quickly find the optimal cost function under a fixed detection interval δ. The algorithm flow is as follows: Figure 3 As shown.

[0058] Value Iterative Optimization Algorithm:

[0059] 1. Input device degradation process Time parameter ωδ, cost parameter C I C F C P C down and allowable error ε;

[0060] 2. Initialize the cost function, let any (n,x,Π) have

[0061] 3. Initialize the iteration count i = 0;

[0062] 4. Calculate the reliability function R(ωδ|nωδ,x,Π) and the transition probability density function g(x′|ωδ,nωδ,x,Π) corresponding to (n,x,Π) according to equations (9) and (10);

[0063] 5. Determine whether x < L is true. If not, then V ω (n,x,Π)=C F +V ω If (0,0,Π) is true, proceed to step 8; otherwise, proceed to step 6.

[0064] 6. According to x′∈[0,L] and equation (12) are calculated

[0065] 7.Judgment Whether it is true or not, if it is true, then it has If not true

[0066] 8.Judgment Check if the condition is true. If it is true, proceed to step 9. If it is false, i = i + 1 and return to step 6.

[0067] 9. Output

[0068] By using the value iteration optimization algorithm, the optimal cost function of a device in state (n,x,Π) under a fixed detection interval can be quickly calculated, the optimal action under any state can be obtained, and the optimal control strategy under a fixed detection interval can be formed.

[0069] Through the above steps, this invention realizes the construction of a device reliability assessment model that can adaptively couple multi-source environmental effects, designs a preventive maintenance strategy planning method based on real-time reliability assessment, studies the heuristic algorithm of the operation and maintenance cost model, and obtains the device reliability assessment method and optimal control strategy planning method under multi-source environmental effects.

[0070] (3) Advantages and benefits:

[0071] 1. This invention addresses the continuous degradation of equipment affected by multi-source environmental coupling effects, constructing a reliability assessment model and an operation and maintenance cost model, and studying an optimal maintenance strategy planning method for equipment under time-varying stochastic environments;

[0072] 2. Compared with existing reliability models that only consider the degradation of the equipment itself, this invention considers the impact of dynamic service environment on equipment degradation, resulting in more accurate evaluation results and stronger applicability.

[0073] 3. Compared with existing static maintenance strategies, this invention designs a dynamic maintenance strategy based on real-time reliability assessment results. It is not only compatible with static threshold maintenance strategies, but also more suitable for equipment with dynamic optimal control strategies under random environmental effects. It has stronger adaptability and better optimization results.

[0074] 4. The heuristic algorithm presented in this invention is simple and fast to compute and has extensive theoretical support.

[0075] 5. The method described in this invention is scientific and its application is closely related to mechanical equipment in dynamic service environments, thus having broad application value. Attached Figure Description

[0076] Figure 1 This diagram illustrates preventative maintenance performed on equipment after a maintenance rule is triggered.

[0077] Figure 2 A diagram illustrating corrective maintenance performed on equipment that failed before the maintenance rules were triggered.

[0078] Figure 3 The flowchart of the proposed heuristic optimization algorithm is shown.

[0079] Figure 4 Example diagram of driver degradation trajectory.

[0080] Figure 5 This is a flowchart of the method of the present invention. Detailed Implementation

[0081] The invention will be further illustrated below with examples.

[0082] The ship's radar actuator is a critical component controlling radar steering, constantly adjusting the radar angle according to commands to ensure normal operation. During ship missions, the actuator may experience unexpected failures due to internal degradation and external environmental shocks, such as structural cracking caused by corrosion. Corrosion-induced cracks are the most common failure mode observed during actuator maintenance, primarily due to corrosion (such as pitting corrosion, crevice corrosion, and stress corrosion). Because ship missions span multiple sea areas and last for extended periods, shipboard equipment is subjected to various environmental stresses, such as temperature and humidity variations, which significantly impact the equipment's degradation process.

[0083] The detection of degradation status of radar actuators is typically performed by crack detection equipment, such as ultrasonic flaw detectors. In this example, the crack propagation process of the actuator is described using the Wiener process, i.e., the equipment degradation at time t is:

[0084] X(t) = x0 + vt + σB(t); where vt is the degradation trajectory affected by environmental effects; σB(t) is the random diffusion term. The main environmental factors affecting the crack propagation rate of the actuator fall into three categories: temperature, humidity, and vibration. Temperature is divided into three states: low temperature, normal temperature, and high temperature, with influence factors on the degradation rate of 1.04, 1, and 1.09, respectively. Humidity is divided into five states from low to high, with influence factors on the degradation rate of 1, 1.01, 1.02, 1.05, and 1.1, respectively. Vibration is divided into five states, with influence factors on the degradation rate of 1, 1.04, 1.07, 1.12, and 1.16, respectively. Specific degradation parameters and maintenance cost parameters of the actuator are shown in Table 1, obtained statistically from historical maintenance records. The minimum time unit is 1 day, denoted as δ = 1. The detection interval is ωδ = 10.

[0085] Table 1 Driver Degradation and Cost Parameters

[0086]

[0087] The method proposed in this invention will be described below with reference to examples:

[0088] Step 1: Single-factor environmental effect modeling;

[0089] Let temperature, humidity, and vibration be defined as environmental effects 1, 2, and 3, respectively. Their corresponding instantaneous state transition matrices are as follows:

[0090]

[0091] according to Calculate the transition probability matrix of the three environmental factors when i∈[1,ω].

[0092] Step 2: Coupling of multiple environmental effects;

[0093] Based on the above description of the effects of three environmental factors on parameter v, the influence effect matrix corresponding to the environmental factors can be obtained as α. k .

[0094]

[0095] The three environmental factors have 3, 3, and 5 states respectively, so Π has π1∈[1,3], π2∈[1,5], and π3∈[1,5]. Calculate the probability matrix of the three environmental factors for all Π states when i∈[1,ω]:

[0096]

[0097] in, For 1×m k The vector, m k π represents the number of possible states for the k-th element. k This represents the k-th element in the environmental state Π, that is, the state of the k-th environmental factor. The π k One element is 1, and the rest are 0. Let be the state transition matrix for the k-th environmental factor experiencing iδ. The expected degradation parameter of the device from iδ to (i+1)δ is:

[0098]

[0099] Extracting the diagonal elements yields the parameter vector E[θ]. τ+iδ |Π].

[0100] Step 3: Reliability modeling and assessment;

[0101] Discretize the cumulative degradation amount with a discrete interval of 0.01. Substitute the calculation results of equations (16)-(18) and the probability density function f(·) of the stochastic process X(t)=x0+vt+σB(t) into equations (9) and (10) to obtain the reliability function and the cumulative degradation probability density distribution of the next detection point in all state spaces.

[0102] Step 4: Maintenance strategy planning;

[0103] Based on the reliability assessment model considering multi-source environmental effects given above, the equipment maintenance strategy is planned as follows:

[0104] (1) Periodic degradation state detection is performed with a detection interval of ωδ = 5, and the detection cost is C. I=500, degradation status detection can: (a) determine whether the equipment has failed; (b) measure the degradation status of the equipment;

[0105] (2) If the system is found not to have failed during degradation status detection, one of the following actions may be taken: (a) not to perform maintenance and allow the equipment to continue in service; (b) to perform preventative maintenance and bear the maintenance costs. P =10000;

[0106] (3) If a system failure is detected during degradation state detection, corrective repairs must be performed, and the repair costs must be borne.

[0107] C F =30000;

[0108] (4) If a failure occurs within the detection interval, downtime costs will be incurred, amounting to C per δ time interval. down =2500.

[0109] Step 5: Calculate maintenance costs;

[0110] At any decision point nωδ, the cumulative degradation state X of the detection equipment is measured. n And obtain the current operating environment state Π of the device. (n,x,Π) constitute a discrete-time Markov chain, whose transition probability is related to the device age. Substituting equations (11) and (14) yields the cost of performing preventative and restorative maintenance in the first iteration;

[0111] Substituting the calculation results of equations (16)-(18), the reliability function R(·) under all state spaces (n,x,Π) obtained in step 3, and the degradation cumulative probability density distribution g(·) of the next detection point into equation (12), we obtain the cost of not performing preventive maintenance in the first iteration; and obtain the optimal value function and optimal strategy through equation (11).

[0112] Step 6: Optimize operation and maintenance costs;

[0113] Substitute the above parameters and calculation results into the value iterative optimization algorithm:

[0114] 1. Input device degradation process Time parameter ωδ, cost parameter C I C F C P C down and allowable error ε;

[0115] 2. Initialize the cost function, let any (n,x,Π) have

[0116] 3. Initialize the iteration count i = 0;

[0117] 4. Based on the results of step 3, input the reliability function R(ωδ|nωδ,x,Π) and the transition probability density function g(x′|ωδ,nωδ,x,Π) corresponding to (n,x,Π);

[0118] 5. Determine whether x < L is true. If not, then V ω (n,x,Π)=C F +V ω If (0,0,Π) is true, proceed to step 8; otherwise, proceed to step 6.

[0119] 6. According to x′∈[0,L] and equation (12) are calculated

[0120] 7.Judgment Whether it is true or not, if it is true, then it has If not true

[0121] 8.Judgment Check if the condition is true. If it is true, proceed to step 9. If it is false, i = i + 1 and return to step 6.

[0122] 9. Output

[0123] By using a value iteration optimization algorithm, the optimal action under any state is obtained, forming the optimal control strategy under a fixed detection interval.

[0124] To further illustrate the effectiveness of the present invention, Figure 4 Ten example diagrams of driver degradation trajectories are provided. Based on the cost parameters in Table 2 and the optimal control strategy obtained in the above steps, the average cost of applying this strategy to the ten degradation trajectories can be calculated. The calculation method is as follows:

[0125] 1. Extract degradation data from the degradation trajectory based on the optimal detection interval;

[0126] 2. Based on the parameter update function in step one, update the degradation parameters of the corresponding detection points;

[0127] 3. Using the control strategy obtained by the proposed value iteration algorithm, calculate the operation and maintenance costs under 10 degradation trajectories;

[0128] Table 2 presents the results of operation and maintenance control using the algorithm proposed in this invention, namely the average operation and maintenance cost obtained by applying it to 10 degradation trajectories, and compares it with the maintenance strategy planning method without parameter updates and the maintenance strategy planning method with fixed maintenance thresholds.

[0129] Table 2. Optimal availability and maintenance schemes of radar drivers under different maintenance strategies.

[0130] Maintenance strategy Detection interval Preventive maintenance threshold Average operating cost The strategy described in this invention 2.4 -- 7841 Strategy of not updating parameters 2.4 -- 8369 Fixed maintenance threshold strategy 3.2 13.4 9107

[0131] The results show that the optimal maintenance strategy obtained by the maintenance strategy planning method proposed in this invention achieves the best average operation and maintenance cost when applied to 10 drives compared to existing strategy planning methods that do not update parameters or have fixed preventive maintenance thresholds. Therefore, this invention addresses the issue of how to scientifically plan maintenance strategies and optimize operation and maintenance costs for equipment considering stochastic environmental effects, particularly in the context of continuously degrading equipment affected by multi-source environmental coupling effects. It constructs a reliability model that considers the impact of environmental effects on equipment degradation, designs a preventive maintenance strategy planning method based on shock environments and degradation states, and conducts research on optimization methods for condition monitoring intervals and preventive maintenance decisions.

[0132] In summary, this invention provides a reliability assessment and maintenance control method based on time-varying coupling of high-dimensional environmental characteristics. This method addresses the continuous performance degradation and failure risk of equipment subjected to multi-source environmental effects under dynamic service environments. It introduces environmental covariate parameters, constructs an adaptive equipment reliability assessment model capable of coupling multiple stochastic environmental effects, formulates a maintenance strategy planning method based on real-time reliability assessment, and designs a joint optimization algorithm for inspection cycles and maintenance control. This method can optimize the average maintenance cost of equipment during long-term operation, providing theoretical and technical support for improving equipment reliability and safety, and reducing equipment operation and maintenance costs.

Claims

1. A reliability evaluation and maintenance control method for time-varying coupling of high-dimensional environment features, characterized in that, Comprising the following steps: Step 1: Single-factor environmental effect modeling; For a single environmental factor, the states are divided into a finite state set E = {e1, e2,..., e N}, e i ∈ E represents the environmental state, and in a time interval Δt, the probability that the environmental state will transition from e i ∈ E to e j ∈ E is represented by P ij (Δt), which has the following properties: Step 2: Multi-factor environmental effect coupling; Consider that the equipment degradation is affected by K environment effects synthetically, and the state set is E k , 0 < k < K; the influence effect matrix of the environment factor is α k ; Step 3: Reliability modeling and evaluation; Device degradation process as a stochastic process The expression; the initial running state of the device is the degradation accumulation 0, and the failure threshold L is set, that is Representing the failure of the device; The device indicates the probability density distribution of the degradation cumulative amount x in the time t since the time τ with the fixed parameter θ τ The probability density distribution of the degradation cumulative amount x in the time t since the time τ with the fixed parameter θ Step 4: Maintenance strategy planning; Based on the given reliability evaluation model considering multi-source environmental effects, the equipment maintenance strategy is planned; Step 5: Operation and maintenance cost calculation; At any decision point nωδ, the accumulated degradation state X of the equipment is detected n and the current operating environment state Π is obtained (n, x, Π). This forms a discrete-time Markov chain, with transition probabilities related to the age of the equipment. At the nth detection point, the optimal equipment operation and maintenance cost is given by: where C ω (n, x, T) represents the expected cost of the equipment not failing and not performing preventive maintenance; Step 6: Operation and maintenance cost optimization; Due to the monotonicity of R(ωδ|nωδ, x, Π) with respect to x, the cost function C ω (n, x, Π) is monotonically increasing with respect to the degradation cumulative x, i.e. there exists a control threshold x * (n, Π) < ξ, when the degradation cumulative exceeds this threshold, performing preventive maintenance is the optimal strategy.

2. The reliability evaluation and maintenance control method of time-varying coupling of environment features in high-dimensional environment according to claim 1, characterized in that: In step 1, when the time interval approaches 0, i.e. Δt→0, the limit expression is: where P ii (Δt) represents the environmental state e i at time Δt, q ij (Δt) represents the probability of staying in the environmental state e i at time Δt, and q i (Δt, e j ) represents the state transition probability density from e i to e and the state transition rate of the environmental state staying in e ; the state transition probability density under the Markov process has stability, and thus the following is obtained: Thus, according to the environmental instantaneous transition rate matrix According to the Kolmogorov forward equation, for any time interval Δt, the state transition probability matrix is 3. The reliability evaluation and maintenance control method of time-varying coupling of environment features in high-dimensional environment according to claim 2, characterized in that: Consider the influence of environmental factors on the degradation process, characterized in the form of an acceleration factor, i.e. for some parameter θ of the set of parameters θ affected by the environmental effect j Under the influence of the environmental state e i with acceleration factor α ij i.e. α is the influence effect matrix of this environmental factor.

4. The reliability evaluation and maintenance control method of time-varying coupling of environment features in high dimensions according to claim 1, characterized in that: In step 2, at time τ, the state probability vector of the kth environmental factor is P k,τ , where the ith element represents the probability that the environmental factor is in the ith state at time τ; due to the time-varying nature of the environmental effect, the parameters of the degradation process also have time characteristics, and under the influence of the kth environmental factor, the parameter set θ affected by the environmental effect is converted into a time-varying parameter set θ k,τ ; the expectation of θ k,τ under the influence of the environmental factor is: wherein is the extended matrix of θ, i.e. diag(θ); which satisfies:

5. The reliability evaluation and maintenance control method of time-varying coupling of environment features in high-dimensional environment according to claim 4, characterized in that: under the influence of the environmental effects, under the influence of a plurality of environmental factors, a set of parameters influenced by the environmental effects θ, converted into a set of time-varying parameters θ τ ; is an extended matrix of θ τ , i.e. diag(θ τ ); the degenerated parameters are represented as: representing the augmented matrix diag(P k,τ α k ); the expectation of the set of equipment degradation parameters under the influence of K environmental effects; extracting the diagonal elements of θ τ to obtain the expected value E[θ τ ].

6. The reliability evaluation and maintenance control method of time-varying coupling of environment features in high-dimensional environment according to claim 1, characterized in that: In step 3, the state transition probability of the kth environmental factor experiencing the environmental state iδ before the next decision point is calculated: in, For 1×m k The vector, m k π represents the number of possible states for the k-th element. k This represents the k-th element in the environmental state Π, that is, the state of the k-th environmental factor. The π k One element is 1, and the rest are 0; Let iδ be the state transition matrix for the k-th environmental factor. Calculate; then, from iδ to (i+1)δ, the expected degradation parameter of the device is: Extracting the diagonal elements gives the parameter vector E [θ τ+iδ |Π].

7. The reliability evaluation and maintenance control method of time-varying coupling of environment features in high dimensions according to claim 6, characterized in that: Due to the time-varying characteristics of environmental effects, the parameter set θ has uncertainty over time; set the minimum time unit of the duration of environmental effects as δ; then at any time τ, the cumulative amount of degradation of the measuring device is X τ , and the environmental state is Π τ , then its reliability within time ωδ is: where E[θ τ+iδ |Π τ ] denotes the expected degradation parameter set at time τ + nδ under the initial environmental state Π τ , and the degradation parameter set at time τ + nδ is derived as The diagonal elements are extracted to obtain x i , which represents the degradation at iδ. The probability density distribution of the cumulative degradation of the equipment at time τ + nδ is given as 8. The reliability evaluation and maintenance control method of time-varying coupling of environment features in high dimensions according to claim 1, characterized in that: In step 4, specifically: (1) performing periodic degradation state detection with a detection interval of δ0 at a cost of C I degradation state detection: (a) determining whether the device has failed; (b) measuring the degradation state of the device (2) If the system is found to be not failed in the degradation state detection, one of the following actions is performed: (a) no repair is performed and the device continues to be in service; (b) preventive repair is performed and the repair cost C is incurred P ; (3) In the degradation state detection, if system failure is found, then corrective maintenance must be performed and the maintenance cost C is incurred F , and C F > C P ; (4) Failure occurs in the detection interval, incurring a shutdown cost, C for each δ time down .

9. The reliability evaluation and maintenance control method of time-varying coupling of environment features in high dimensions according to claim 1, characterized in that: In step 5, specifically: where e -rδ represents the discount factor; E[V δ (n + 1, x', Π') | Π] represents the expected equipment repair cost at the next inspection point given the state (n + 1, x') and the set of environmental factors Π; P k,ω Π) represents the probability of the state of the kth environmental factor at the next inspection point, then we have: wherein, represents P k,ω (Π) the ith k element, m1...m K represent the number of possible states for the first through Kth environmental factors, respectively; P ω (n, x, T) represents the expected cost of performing preventive maintenance in the event of no failure of the equipment, and is given by: P ω (n,x,Π) = C P +V ω (0,0,Π) C F +V ω (0,0,Π) represents the cost the device incurs in case of failure at the detection point.

10. The reliability evaluation and maintenance control method of time-varying coupling of environment features in high dimensions according to claim 1, characterized in that: In step 6, since the cost function calculation is too complex, a value iteration optimization algorithm is designed to find the optimal cost function under a fixed detection interval δ, and the value iteration optimization algorithm is: 6.1 Input device degradation process time parameter ω, cost parameter C I , C F , C P , C down and an allowed error ε; 6.2 Initialize the cost function, let any (n, x, Π) have 6.3 Initialize the iteration number i = 0; 6.4 Calculate the reliability function R(ωδ|nωδ, x, Π) and the transition probability density function g(x′|ωδ, nωδ, x, Π) corresponding to (n, x, Π); 6.5 Determine if x < L, if not, V = V + V ω (n, x, Π) = C F + V ω (0, 0, Π), go to step 6.8, if yes, go to step 6.6; 6.6 According to and C ω (n, x, Π) computation 6.7 Determine if the condition is true, then if the condition is false, then 6.8 decision is true, then go to step 6.9, otherwise, i = i + 1, and return to step 6.6; 6.9 Output Through the value iteration optimization algorithm, the optimal cost function of the equipment in state (n, x, Π) under a fixed detection interval is calculated, the optimal action under any state is obtained, and the optimal control strategy under a fixed detection interval is formed.

Images