Adaptive Maintenance System and Method for Mechanical Equipment for Dynamic Working Conditions

Abstract

The present invention provides an adaptive maintenance system and method for mechanical equipment facing dynamic working conditions, and makes maintenance decisions for mechanical equipment through three modules: degradation modeling of equipment under dynamic working conditions, updated prediction of conditional reliability, and formulation of adaptive maintenance decisions. Different from traditional maintenance strategies based on degradation states or failure rates, the present invention makes decision judgments on the reliability of equipment, takes into account different failure modes of the equipment and the influence of dynamic working conditions on reliability, and adopts an adaptive monitoring interval, effectively improving the operation economy of the equipment and the service life of the equipment, with strong applicability and high flexibility.

Description

Technical Field

[0001] The present invention belongs to the field of equipment maintenance, and particularly relates to an adaptive maintenance system and method for mechanical equipment under dynamic working conditions. Background Art

[0002] With the rapid development of intelligent manufacturing technology, higher requirements are put forward for the reliability and cost of mechanical equipment. Mechanical equipment usually operates under dynamic working conditions, and various environmental factors such as load, temperature, and humidity will have a significant impact on the performance and reliability of mechanical equipment. Mechanical equipment will experience different failure modes during degradation, and there are competitive risks for these failure modes. Therefore, mechanical equipment with failure competition risks under dynamic working conditions needs to consider effective maintenance strategies to meet the requirements of reliable operation and maintenance. Condition-based maintenance (CBM) can reduce unnecessary maintenance, lower operating costs and downtime, and improve safety and reliability at the same time, so it has attracted more and more attention from the industry and academia.

[0003] CBM can monitor the health status of the mechanical system in real time and make maintenance decisions based on the condition monitoring information collected by sensors. This maintenance strategy can not only ensure the safe and reliable operation of the equipment, but also reduce the operation and maintenance costs through maintenance decisions. At present, maintenance decisions are all made based on the degradation state or failure rate of the equipment under constant working conditions, and these methods do not well reflect the true reliability of the equipment. Generally speaking, the reliability of the equipment is relatively high in the initial stage of operation. As the operation time increases, the reliability of the equipment gradually decreases, and it is more likely to fail. Moreover, due to different degradation modes of mechanical equipment under different working conditions, the reliability will change non-monotonically. Therefore, the assumptions of constant working conditions and monotonic deterioration in traditional maintenance strategies are not sufficient to reflect the change of equipment status.

[0004] In summary, there is currently no effective solution for the CBM maintenance strategy of mechanical equipment with failure competition risks under dynamic working conditions. The reliability-based adaptive maintenance strategy, because it can more accurately reflect the change of reliability and reduce costs, should be widely applied in actual engineering. Correspondingly, there is a technical need in this field to develop an adaptive maintenance strategy for mechanical equipment with failure competition risks under dynamic working conditions based on reliability. Summary of the Invention

[0005] The purpose of the present invention is to provide an adaptive maintenance system and method for mechanical equipment under dynamic working conditions, and provide at least the advantages described later.

[0006] Different from traditional maintenance strategies that are based on degradation states or failure rates, the present invention makes decision judgments on the reliability of equipment. At the same time, it takes into account different failure modes of the equipment and the impact of dynamic operating conditions on reliability, and adopts an adaptive monitoring interval, effectively improving the operating economy of the equipment and the service life of the equipment, with strong applicability and high flexibility.

[0007] The technical solution of the present invention is as follows:

[0008] An adaptive maintenance system for mechanical equipment facing dynamic operating conditions, which includes:

[0009] A degradation modeling module for dynamic operating condition equipment, which establishes a degradation model based on the historical maintenance data of the mechanical equipment to be maintained, and selects a random factor from the degradation model to represent the change process of the dynamic operating conditions;

[0010] A conditional reliability prediction and update module, which collects the condition monitoring data of the mechanical equipment to be maintained, and uses the rectangular approximation method to calculate and obtain a health assessment index reflecting the health information of the equipment, takes it as the conditional reliability, and updates it according to the change of the condition monitoring interval;

[0011] An adaptive maintenance decision-making module, which pre-stores a warning threshold W 1 and a maintenance threshold W 2 , W 1 >W 2 , and selects different monitoring intervals for adaptive maintenance according to the current conditional reliability.

[0012] An adaptive maintenance method for mechanical equipment facing dynamic operating conditions, which includes the following steps:

[0013] Establish a degradation model based on the historical maintenance data of the mechanical equipment to be maintained, and select a random factor from the degradation model to represent the change process of the dynamic operating conditions;

[0014] Collect the condition monitoring data of the mechanical equipment to be maintained, and use the rectangular approximation method to calculate and obtain a health assessment index reflecting the health information of the equipment, take it as the conditional reliability, and update it according to the change of the condition monitoring interval;

[0015] Pre-store a warning threshold W 1 and a maintenance threshold W 2 , W 1 >W 2 , and select different monitoring intervals for adaptive maintenance according to the current conditional reliability.

[0016] Preferably, in the above-mentioned adaptive maintenance method for mechanical equipment facing dynamic operating conditions,

[0017] When the conditional reliability level of the device is higher than the warning threshold, a long interval Δ is adopted. 1 ; when the conditional reliability level of the device is lower than the warning threshold, the monitoring interval becomes smaller to Δ 2 , and the monitoring frequency of the device increases; when the conditional reliability of the device returns above the warning threshold again, the monitoring interval changes from Δ 2 back to Δ 1 ; when the conditional reliability level of the device is lower than the maintenance threshold of the device, preventive maintenance is performed on the device; when the device fails, failure replacement is performed on the device.

[0018] Preferably, in the adaptive maintenance method for mechanical equipment facing dynamic working conditions,

[0019] it is assumed that the change of the working condition follows a normal distribution, and there are two failure modes for the mechanical equipment to be maintained, namely soft failure and hard failure.

[0020] Soft failure means that the degradation value of the mechanical equipment exceeds the preset failure threshold; and when the mechanical equipment fails randomly due to factors such as external impact and hidden manufacturing defects, the failure mode of the equipment is a hard fault.

[0021] Preferably, in the adaptive maintenance method for mechanical equipment facing dynamic working conditions,

[0022] A Wiener process is used to model the degradation process of the mechanical equipment, and the drift parameter is selected as a random factor to represent the influence of the dynamic working condition; when the degradation value exceeds the preset failure threshold, the equipment will have a soft failure. The mathematical expression of this Wiener process is:

[0023] X(t,λ t ) = X(0) + λ t t + σB(t)

[0024] where X(0) and σ are both constants, B(t) is a standard Brownian process, λ t is a random factor representing the dynamic working condition, and its distribution follows a normal distribution; the parameters Θ = (μ λ ,σ λ 2 ,σ) of the degradation model can be solved by the maximum likelihood estimation algorithm.

[0025] The system hard failure rate is represented by a proportional hazards model, and its covariates are represented by a Wiener process with a random factor to represent the influence of the degradation of the mechanical equipment on the failure rate. Its mathematical expression is:

[0026]

[0027] where h 0 (t) is the baseline hazard function at time t, and a Weibull distribution is adopted, that is, h0 (t) = βt β-1 / α β , where γ is a regression parameter that depends only on the degradation value X(t,λ t ).

[0028] Preferably, in the adaptive maintenance method for mechanical equipment facing dynamic working conditions, the calculation process of the conditional reliability is as follows:

[0029] Set the failure threshold of the equipment as w, divide the degradation value [0, w] into M equal parts, and define the state as the soft failure state M when it exceeds w; convert the continuous degradation process into a Markov chain, and its state space is Ω = {0, 1, …, M - 1, M}. Divide the monitoring interval into small enough intervals δ, and define the current monitoring interval as t ω = ωδ.

[0030] Consider the one-step transition probability from degradation state i to j, i, j ∈ Ω as:

[0031] Λ ij (ωδ)

[0032] = P(ζ > (ω + 1)δ, X((ω + 1)δ,λ (ω+1)δ ) = j|ζ > ωδ, X(ωδ,λ ωδ ) = i)

[0033] = P(X((ω + 1)δ,λ (ω+1)δ ) = j|(ω + 1)δ, X(ωδ,λ ωδ ) = i)

[0034] ·P(ζ > (ω + 1)δ|ζ > ωδ, X(ωδ,λ ωδ ) = i)

[0035] Use the matrix P to represent the state transition probability matrix of each monitoring point during the entire life cycle:

[0036]

[0037] where I is the (M + 1) × (M + 1) identity matrix, 0 is the (M + 1) × (M + 1) zero matrix, and U is the unit vector containing (M + 1) elements;

[0038] Then, the formula for conditional reliability can be obtained through the matrix P:

[0039] R(rδ|ζ > ωδ, X(ωδ,λ ωδ ) = i)

[0040] = P(ζ > (ω + r)δ|ζ > ωδ, X(ωδ,λ ωδ ) = i)

[0041] = 1 - π i (ωδ)(I - B r )U

[0042] In the formula, π i (ωδ) = (0, …, 0, 1, 0, …, 0) is a row vector containing 1×(M + 1)N elements, where the ω(M + 1)+i-th element is 1 and the rest are 0.

[0043] Preferably, in the adaptive maintenance method for mechanical equipment facing dynamic working conditions, to achieve the minimum operation and maintenance cost per unit time, according to renewal theory, this problem is equivalent to finding the optimal control strategy such that:

[0044]

[0045] where CC and CL respectively represent the total operation and maintenance cost and the time length of the equipment in one cycle, and the maintenance strategy uses an algorithm based on semi-Markov decision process to solve the optimal control threshold and monitoring interval.

[0046] Preferably, in the adaptive maintenance method for mechanical equipment facing dynamic working conditions, the specific operation process of the semi-Markov decision process is as follows:

[0047] First, determine the state space of the SMDP, divide the value range [0, 1] of the conditional reliability into K equal parts,

[0048] W 1 , W 2 ∈{1, 2, …, K}; assume that at the n 1 +n 2 -th sampling, the conditional reliability of the equipment is greater than W 1 , then it is defined as the state (i, n 1 +n 2 ), and the state set of this state is S 1 = {(i, n 1 +n 2 ): R(i, n 1 Δ 1 +n 2 Δ 2 ) > W 1}, where the first element represents the degradation state value of the equipment, that is the second element represents the sampling times; similarly,

[0049] S 2 = {(j, n 1 +n 2 ): W 2 <R(j, n 1 Δ1 +n 2 Δ 2 ) ≤ W 1} represents the state set where the equipment condition reliability is between two thresholds. In particular, when i, j = M, that is, when the equipment has a soft failure, the equipment is replaced due to failure; when the equipment condition reliability is lower than the warning threshold, the equipment undergoes preventive maintenance, defined as S 3 = {PM}; when the equipment fails, that is, when a hard failure occurs, the equipment is in the failure state S 4 = {F}, and failure replacement should be carried out; both preventive maintenance and failure replacement will return the equipment to the brand-new state S 0 = {(0, 0)}. Therefore, the state space of the SMDP is defined as S = S 0 ∪ S 1 ∪ S 2 ∪ S 3 ∪ S 4 ;

[0050] Secondly, define and calculate three elements in the SMDP, the transition probability, the expected sojourn time, and the expected cost:

[0051] P r,k : The probability that the current equipment is in state r ∈ S and transitions to state k ∈ S at the next decision moment;

[0052] τ r : The expected sojourn time of the equipment in state r ∈ S from the current decision moment to the next decision moment;

[0053] C r : The expected cost of the equipment in state r ∈ S from the current decision moment to the next decision moment;

[0054] Finally, for a given control policy the operation and maintenance cost of the equipment can be obtained through the following linear equation:

[0055]

[0056] V j = 0, for any state, j ∈ S.

[0057] The present invention has the following beneficial effects:

[0058] During the operation of mechanical equipment, it is affected by various internal and external random factors, resulting in varying degrees of changes in the performance of the mechanical equipment, thus affecting the reliability of the mechanical equipment. The present invention takes into account various failure modes under dynamic working conditions, establishes a Wiener process with random factors to describe the soft failure model, uses the proportional hazards model to describe the hard failure rate, and calculates the conditional reliability of the mechanical equipment through the matrix approximation method, which better solves the problem of calculating the conditional reliability under dynamic working conditions. Based on the adaptive maintenance model, the optimal control threshold and monitoring interval of the equipment are solved, and the equipment is monitored and maintained accordingly, which is beneficial to reasonably monitor the operation status of the equipment and effectively reduce the downtime loss and maintenance cost.

[0059] Other advantages, objectives, and features of the present invention will be partially reflected by the following description and partially understood by those skilled in the art through the research and practice of the present invention. Brief Description of the Drawings

[0060] Figure 1 It is a structural block diagram of an embodiment of the adaptive maintenance system for mechanical equipment facing dynamic working conditions provided by the present invention;

[0061] Figure 2 It is a flowchart of an embodiment of the adaptive maintenance method for mechanical equipment facing dynamic working conditions provided by the present invention;

[0062] Figure 3 It is a historical degradation data diagram in an embodiment of the adaptive maintenance system and method for mechanical equipment facing dynamic working conditions provided by the present invention;

[0063] Figure 4 It is a soft failure data diagram in an embodiment of the adaptive maintenance system and method for mechanical equipment facing dynamic working conditions provided by the present invention;

[0064] Figure 5 It is a hard failure data diagram in an embodiment of the adaptive maintenance system and method for mechanical equipment facing dynamic working conditions provided by the present invention;

[0065] Figure 6 It is an implementation process diagram of the adaptive monitoring interval in an embodiment of the adaptive maintenance system and method for mechanical equipment facing dynamic working conditions provided by the present invention;

[0066] Figure 7 It is a flowchart of the maintenance strategy in an embodiment of the adaptive maintenance system and method for mechanical equipment facing dynamic working conditions provided by the present invention;

[0067] Figure 8 It is a decision-making process diagram of soft failure data maintenance in an embodiment of the adaptive maintenance system and method for mechanical equipment facing dynamic working conditions provided by the present invention;

[0068] Figure 9 This is a diagram of the hard failure data maintenance decision-making process in an embodiment of the adaptive maintenance system and method for mechanical equipment facing dynamic working conditions provided by the present invention. Detailed implementation manners

[0069] The following further elaborates on the present invention with reference to the accompanying drawings, so that those skilled in the art can implement it according to the description in the specification.

[0070] As Figure 1 shown, the present invention provides an adaptive maintenance system for mechanical equipment facing dynamic working conditions, which includes:

[0071] A degradation modeling module for dynamic working condition equipment, which establishes a degradation model based on the historical maintenance data of the mechanical equipment to be maintained, and selects a random factor from the degradation model to represent the change process of the dynamic working condition;

[0072] A conditional reliability prediction and update module, which collects the condition monitoring data of the mechanical equipment to be maintained, calculates the health assessment index reflecting the equipment health information by using the rectangular approximation method, takes it as the conditional reliability, and updates it according to the change of the condition monitoring interval;

[0073] An adaptive maintenance decision-making module, which pre-stores the warning threshold W 1 and the maintenance threshold W 2 , W 1 >W 2 , and performs adaptive maintenance by selecting different monitoring intervals according to the current conditional reliability.

[0074] As Figure 2 shown, the present invention also provides an adaptive maintenance method for mechanical equipment facing dynamic working conditions, which includes the following steps:

[0075] 1) Establish a degradation model of the mechanical equipment based on historical data and perform parameter estimation. In the degradation model, a random factor is used to represent the change process of the dynamic working condition, a proportional hazards model with a random factor is proposed to represent the equipment failure rate, and finally the parameters of the degradation model are estimated by the maximum likelihood estimation algorithm.

[0076] Assume that the mechanical equipment under dynamic working conditions is subjected to condition monitoring at discrete time intervals (Δ, 2Δ,...). Considering the competing risks of hard and soft failures existing in the mechanical equipment under dynamic working conditions, a Wiener process with a random factor is used to model the degradation, and its mathematical expression is:

[0077] X(t, λ t ) = X(0) + λ t t + σB(t)

[0078] where X(0) and σ are both constants, representing the initial degradation value and the diffusion coefficient respectively, B(t) is a standard Brownian process, and λ t is the drift coefficient, which is used as a random factor to represent the change of working conditions, and its distribution follows a normal distribution, λ t ~N(μ λ , σ λ 2 ).

[0079] The hard failure rate of the equipment is represented by a proportional hazards model, which includes both age and degradation data. The covariates of the proportional hazards model are represented by a Wiener process with a random factor to represent the system degradation state, and its mathematical expression is:

[0080]

[0081] where h 0 (t) is the baseline hazard function at time t, which follows a Weibull distribution, i.e., h 0 (t) = βt β-1 / α β , γ is the regression parameter, which only depends on the degradation value X(t, λ t ). The parameters Θ = (μ λ , σ λ 2 , σ) of the degradation model and the parameters in the proportional hazards model can be solved by the maximum likelihood estimation algorithm.

[0082] 2) Conduct condition monitoring on the operating equipment, and use the matrix approximation method to obtain the health assessment index reflecting the equipment health information, i.e., the conditional reliability, for the collected condition monitoring information, and update it according to the change of the monitoring interval.

[0083] First, set the failure threshold of the equipment as w, divide the degradation value [0, w] into M equal parts, and define the state as the soft failure state M when it exceeds w. This approximation method transforms the continuous degradation process into a Markov chain, and its state space is Ω = {0, 1,..., M - 1, M}. The transition of the degradation state is random and may span multiple states in one monitoring interval.

[0084] Second, divide the monitoring interval into small enough intervals δ. When the system runs for more than time T = Nδ, the equipment stops working. Define the current monitoring interval as t ω = ωδ.

[0085] Finally, considering the one-step transition probability of the degradation state from i to j, i, j ∈ Ω is:

[0086] Λ ij (ωδ)

[0087] = P(ζ > (ω + 1)δ, X((ω + 1)δ, λ (ω+1)δ ) = j | ζ > ωδ, X(ωδ, λ ωδ ) = i)

[0088] = P(X((ω + 1)δ, λ (ω+1)δ ) = j | (ω + 1)δ, X(ωδ, λ ωδ ) = i)

[0089] ·P(ζ > (ω + 1)δ | ζ > ωδ, X(ωδ, λ ωδ ) = i)

[0090] The former can be solved by the degradation characteristics of the Wiener process with a random factor. Within any monitoring interval [(k - 1)Δ, kΔ], k ∈ N, the degradation amount of the mechanical equipment is independently and identically distributed and follows a normal distribution, that is, X(k Δ , λ kΔ ) - X((k - 1)Δ, λ (k-1)Δ ) ~ N(λΔ, σ 2 Δ), and the specific formula is:

[0091]

[0092] where the definitions of lb and ub are as follows:

[0093] When i = 0, j ∈ {1, …, M - 1},

[0094] When i = 0, j = M,

[0095] When i, j ∈ {1, …, M - 1}, and j > i,

[0096] When i, j ∈ {1, …, M - 1}, and j < i,

[0097] When i ∈ {1, …, M - 1}, and j = M,

[0098] In particular, when 0 ≤ i = j ≤ M, P ii = 1 - ∑ j≠i P ij ; when i = j = M, P MM = 1.

[0099] The latter can be approximately calculated as:

[0100]

[0101] Use the matrix P to represent the state transition probability matrix of each monitoring point throughout the life cycle:

[0102]

[0103] Where I is the (M + 1)×(M + 1) identity matrix, 0 is the (M + 1)×(M + 1) zero matrix, and U is the unit vector containing (M + 1) elements.

[0104] For the sake of simplicity in calculation, we partition the matrix P:

[0105]

[0106] Since the matrix P is a stochastic transition probability matrix and the sum of each row is 1, therefore,

[0107]

[0108] Where, (I - B r )U represents the probability that the device undergoes a hard failure within the next rδ time. Then, the formula for the conditional reliability can be obtained through the matrix P:

[0109] R(rδ|ζ>ωδ,X(ωδ,λ ωδ )=i)

[0110] =P(ζ>(ω + r)δ|ζ>ωδ,X(ωδ,λ ωδ )=i)

[0111] =1 - π i (ωδ)(I - B r )U

[0112] In the formula, π i (ωδ)=(0,…,0,1,0,…,0) is a row vector containing 1×(M + 1)N elements, where the ω(M + 1)+i-th element is 1 and the rest are 0.

[0113] When the monitoring interval changes adaptively, the matrix P is updated, thereby obtaining the updated conditional reliability.

[0114] 3) Establish an adaptive maintenance model where the monitoring interval changes adaptively with the change in reliability. Taking the minimum equipment operation and maintenance cost per unit time as the optimization objective, find the optimal decision variables in the semi-Markov decision process to obtain the optimal maintenance strategy, and finally perform adaptive maintenance on the equipment based on the conditional reliability.

[0115] First, an adaptive maintenance model for mechanical equipment is established. The adaptive maintenance model refers to making maintenance decisions on equipment with an adaptive monitoring interval based on conditional reliability, that is, the monitoring interval changes adaptively with the change of conditional reliability. This model includes two control thresholds and two monitoring intervals. Among them, the control thresholds are divided into a warning threshold W 1 and a maintenance threshold W 2 (W 1 >W 2 ), and the monitoring intervals are divided into a long interval Δ 1 and a short interval Δ 2 (Δ 1 >Δ 2 ). When the conditional reliability level of the equipment is higher than the warning threshold, the long interval Δ 1 is adopted; when the conditional reliability level of the equipment is lower than the warning threshold, the monitoring interval becomes smaller to Δ 2 , and the monitoring frequency of the equipment increases; when the conditional reliability of the equipment returns above the warning threshold again, the monitoring interval changes back from Δ 2 to Δ 1 ; when the conditional reliability level of the equipment is lower than the maintenance threshold of the equipment, preventive maintenance is carried out on the equipment; when the equipment fails, failure replacement is carried out on the equipment.

[0116] The goal of the maintenance model is to achieve the minimum operation and maintenance cost per unit time. According to renewal theory, this problem is equivalent to finding the optimal control strategy such that:

[0117]

[0118] where CC and CL respectively represent the total operation and maintenance cost and the time length of the equipment in one cycle. The maintenance strategy uses a policy iteration algorithm based on the SMDP framework to solve the optimal control threshold and monitoring interval. The specific implementation steps of the policy iteration algorithm of the SMDP framework are as follows:

[0119] First, determine the state space of the SMDP. Divide the value range [0,1] of the conditional reliability into K equal parts,

[0120] W 1 ,W 2 ∈{1,2,…,K}. Assume that at the n 1 +n 2 -th sampling, the conditional reliability of the equipment is greater than W 1 , then it is defined as the state (i,n 1 +n 2 ), and the state set of this state is S 1 ={(i,n 1 +n 2 ):R(i,n 1 Δ1 +n 2 Δ 2 )>W 1}, where the first element represents the degradation state value of the device, i.e., the second element represents the number of sampling times; similarly,

[0121] S 2 ={(j,n 1 +n 2 ):W 2 <R(j,n 1 Δ 1 +n 2 Δ 2 )≤W 1} represents the state set where the conditional reliability of the device is between two thresholds. In particular, when i,j = M, i.e., when the device has a soft failure, the device is replaced due to failure; when the conditional reliability of the device is lower than the warning threshold, the device undergoes preventive maintenance, defined as S 3 ={PM}; when the device fails, i.e., has a hard failure, the device is in the failure state S 4 ={F}, and failure replacement should be carried out; both preventive maintenance and failure replacement will return the device to the brand-new state S 0 ={(0,0)}. Therefore, the state space of the SMDP is defined as S = S 0 ∪S 1 ∪S 2 ∪S 3 ∪S 4 .

[0122] Secondly, define and calculate three elements in the SMDP, the transition probability, the expected sojourn time, and the expected cost:

[0123] P r,k : The probability that the current device is in state r ∈ S and transitions to state k ∈ S at the next decision moment;

[0124] τ r : The expected sojourn time of the device in state r ∈ S from the current decision moment to the next decision moment;

[0125] C r : The expected cost of the device in state r ∈ S from the current decision moment to the next decision moment;

[0126] The calculation formula for the transition probability is as follows:

[0127] When i ≠ M,

[0128]

[0129]

[0130]

[0131] where i′ is the covariate value at which the reliability is lower than the maintenance threshold W 2 .

[0132] When j ≠ M

[0133]

[0134]

[0135]

[0136]

[0137] When i, j = M

[0138]

[0139] P PM(0,0) = 1

[0140] P F(0,0) = 1

[0141] The calculation formula for the expected sojourn time is as follows:

[0142]

[0143]

[0144]

[0145] τ PM = T P

[0146] τ F = T F

[0147] where Γ(i, n 1 + n 2 ) is the expected sojourn time of the device operating state within a long monitoring interval,

[0148] Γ(j, n 1 + n 2 ) is the expected sojourn time of the device operating state within a short monitoring interval, T P and T F are the times spent on preventive maintenance and failure replacement respectively.

[0149] The calculation formula for the expected cost is as follows:

[0150]

[0151]

[0152]

[0153] C PM = C P

[0154] C F = C F

[0155] where C S , C P , C F are the costs of sampling, preventive maintenance, and failure replacement, respectively.

[0156] Finally, for a given control strategy the operation and maintenance cost of the equipment can be obtained by the following linear equation:

[0157]

[0158] V j = 0, for any state, j ∈ S

[0159] The minimum value of the operation and maintenance cost per unit time can be calculated by an iterative algorithm, thereby obtaining the optimal control strategy

[0160] After obtaining the conditional reliability of the equipment based on the state monitoring information, online maintenance of the equipment can be carried out, the adaptive monitoring interval can be adopted according to the reliability, and maintenance decisions can be made.

[0161] A case study is carried out using the bearing vibration signal. A bearing is a mechanical component that restricts relative motion and reduces friction between moving parts. High-speed rotation of the rolling elements will cause rotational wear, and the wear will cause the bearing to deform and increase vibration. Thus, it can be seen that the degradation signal based on vibration can indirectly reflect rotational wear. Therefore, it is reasonable to evaluate the health status of the bearing by measuring the vibration signal. For the external environment, the load applied to the bearing may increase rotational wear, and it is reasonably assumed that the load, as a dynamic working condition, follows a normal distribution.

[0162] First, an offline model of the equipment is established. The degradation data is obtained by monitoring and tracking the change of the vibration level over time, and it is collected every 2 minutes. Through monitoring, two failure modes of hard failure and soft failure occur in the bearing. A total of 10 pieces of degradation data are collected in the experiment, as Figure 3 shown. Figure 4 andFigure 5 Two pieces of failure data are respectively shown. Figure 4 For historical data #6, the degradation value exceeds the failure threshold of degradation at 138 minutes and is regarded as a soft failure. Figure 5 For historical data #10, the bearing has a random failure at 94 minutes and is regarded as a hard failure.

[0163] Assume that the degradation data follows a Wiener process:

[0164] X(t,λ t ) = X(0) + λ t t + σB(t)

[0165] Its failure rate model follows a proportional hazards model:

[0166]

[0167] The parameter values of the degradation model obtained by maximum likelihood estimation are: α = 500.34, β = 3.35, γ = 0.64 and Θ = (μ λ ,σ λ 2 ,σ) = (5.859e-5, 2.7019e-7, 4.601e-2).

[0168] Then, after obtaining the new degradation value, the degradation path is evenly divided into M = 10 parts, the failure threshold of degradation is w = 0.02546 Vrms, the time is divided by δ = 2, and the maximum life is T = 200.

[0169] The implementation process of the adaptive monitoring interval in the adaptive maintenance model is as Figure 6 shown. Define the control threshold in the maintenance strategy as W 1 ,W 2 ∈[0,1], the monitoring interval is defined as Δ 1 = r 1 δ, Δ 2 = r 2 δ, and the specific maintenance strategy flowchart is as Figure 7 shown. According to renewal theory, the problem of minimizing the long-term average operation and maintenance cost is equivalent to finding the optimal control strategy such that:

[0170]

[0171] To find the optimal control strategy and the minimum operation and maintenance cost, first define the SMDP framework, evenly divide the reliability [0,1] into K = 10 parts, and then define the time cost parameter in the maintenance model as C S = 10, C P = 200, C F = 500, TP = 40 and T F = 60. Three elements of the SMDP can be obtained through these parameters.

[0172] Transition probability:

[0173] When i ≠ M,

[0174]

[0175]

[0176]

[0177] When j ≠ M,

[0178]

[0179]

[0180]

[0181]

[0182] When i, j = M,

[0183]

[0184] P PM(0,0) = 1

[0185] P F(0,0) = 1

[0186] Expected sojourn time:

[0187]

[0188]

[0189]

[0190] τ PM = T P

[0191] τ F = T F

[0192] Expected cost:

[0193]

[0194]

[0195]

[0196] C PM = E(cost|PM) = C P

[0197] C F = E(cost|F) = C F

[0198] For a given control strategy The operation and maintenance cost of the device Can be obtained through the following linear equation:

[0199]

[0200] V j = 0, for any state, j ∈ S

[0201] After iterative calculation, the optimal control strategy is The corresponding minimum long-term expected average cost is

[0202] Finally, after obtaining the optimal maintenance strategy of this solution, the maintenance decision of the bearing can be made. The maintenance decision-making process of the two failure history data of the bearing is provided in the case, such as Figure 8 and 9 shown.

[0203] Figure 8 Shows the maintenance decision-making process for the soft failure data #6, whose failure time is 138 minutes. At the beginning of operation, the bearing conditional reliability is relatively high, and a long monitoring interval Δ 1 monitoring system is adopted. At the 5th monitoring point, the conditional reliability is lower than the warning threshold W 1 , and the monitoring interval is converted to a short monitoring interval Δ 2 . At the 6th monitoring point, the reliability is higher than W 1 again, then the monitoring interval returns to Δ 1 . At the 7th monitoring point, the bearing conditional reliability is lower than the warning threshold W 1 again, and it is re-converted to the short monitoring interval Δ 2 . The 8th monitoring point is higher than the warning threshold W 1 , and it is converted to Δ 1 . After the 9th monitoring point, Δ 2 is always used for monitoring until the 12th monitoring point, when the bearing conditional reliability is lower than the maintenance threshold W 2 , and preventive maintenance is performed.

[0204] Figure 9 Shows the maintenance decision-making process for the hard failure data #10, whose failure time is 96 minutes. At the 5th monitoring point, the bearing conditional reliability is lower than the warning threshold W1 and the monitoring interval changes from Δ 1 to Δ 2 . At the 6th monitoring point, the reliability is higher than the warning threshold W again 1 and the monitoring interval changes from Δ 2 to Δ 1 . Preventive maintenance is performed at the 7th monitoring point.

[0205] Using the above technical method, the present invention provides an adaptive maintenance method and system for mechanical equipment facing dynamic working conditions, which can perform degradation modeling on historical data, solve the conditional reliability of mechanical equipment under dynamic working conditions through condition monitoring data, and determine maintenance decisions according to the obtained conditional reliability, optimized control thresholds and monitoring intervals. This method has been verified by algorithms and case tests have been carried out using real bearing vibration signals. The results show that this maintenance strategy can take appropriate maintenance measures to prevent the occurrence of faults. While improving the equipment performance and safety, it also saves the operation and maintenance costs.

[0206] The present invention belongs to the technical field related to equipment maintenance, and discloses an adaptive maintenance system and method for mechanical equipment facing dynamic working conditions. The adaptive maintenance system includes three modules: a degradation modeling module for dynamic working condition equipment, an update and prediction module for conditional reliability, and a decision-making module for adaptive maintenance. The method specifically includes the following steps: (1) Degradation modeling of dynamic working condition equipment: Establish a degradation model of mechanical equipment based on historical data and perform parameter estimation. A random factor is used in the degradation model to represent the change process of dynamic working conditions, and a proportional hazard model with a random factor is proposed to represent the equipment failure rate. Finally, the parameters of the degradation model are estimated by the maximum likelihood estimation algorithm; (2) Prediction and update of conditional reliability: Monitor the status of the operating equipment, and use the matrix approximation method for the collected status monitoring information to obtain a health assessment index reflecting the equipment health information, that is, conditional reliability, and update it according to the change of the monitoring interval; (3) Decision-making for adaptive maintenance: Establish an adaptive maintenance model, and the monitoring interval changes adaptively with the change of reliability. With the minimum equipment operation and maintenance cost per unit time as the optimization goal, the optimal decision variable is obtained in the semi-Markov decision process to obtain the optimal maintenance strategy. Finally, adaptive maintenance is performed on the equipment based on the conditional reliability. The present invention effectively improves the equipment operation economy and equipment service life, and has strong applicability and high flexibility.

[0207] Although the embodiments of the present invention have been disclosed as above, it is not limited to the applications listed in the specification and embodiments. It can be fully applied to various fields suitable for the present invention. For those familiar with the field, additional modifications can be easily made. Therefore, without departing from the general concept defined by the claims and the equivalent scope, the present invention is not limited to specific details.

Claims

1. An adaptive maintenance method for mechanical equipment facing dynamic working conditions, characterized in that, it includes the following steps: Establish a degradation model based on the historical maintenance data of the mechanical equipment to be maintained, and select a random factor from the degradation model to represent the change process of the dynamic working conditions; Collect the condition monitoring data of the mechanical equipment to be maintained, and use the rectangular approximation method to calculate the health assessment index reflecting the equipment health information, which is used as the conditional reliability and updated according to the change of the condition monitoring interval; Pre-stored warning threshold W for conditional reliability 1 and maintenance threshold W 2 , W 1 > W 2 , and select different monitoring intervals according to the current conditional reliability; The calculation process of the conditional reliability is as follows: Set the failure threshold of the equipment as w, divide the degradation value [0, w] into M equal parts, and define the state as the soft failure state M when it exceeds w; Convert the continuous degradation process into a Markov chain, and its state space is Ω = {0, 1, …, M - 1, M}; Divide the monitoring interval into small enough intervals δ, and define the current monitoring interval as t ω = ωδ; Consider the one-step transition probability from the degradation state i to j, i, j ∈ Ω as: Λ ij (ωδ) = P(ζ > (ω + 1)δ, X((ω + 1)δ, λ (ω+1)δ ) = j | ζ > ωδ, X(ωδ, λ ωδ ) = i) = P(X((ω + 1)δ, λ (ω+1)δ ) = j | (ω + 1)δ, X(ωδ, λ ωδ ) = i) ·P(ζ > (ω + 1)δ | ζ > ωδ, X(ωδ, λ ωδ ) = i) Use the matrix P to represent the state transition probability matrix of each monitoring point during the entire life cycle: where I is the (M + 1) × (M + 1) identity matrix, 0 is the (M + 1) × (M + 1) zero matrix, and U is the unit vector containing (M + 1) elements; Then the formula for the conditional reliability can be obtained through the matrix P: R(rδ|ζ>ωδ,X(ωδ,λ ωδ ) = i) =P(ζ > (ω + r)δ | ζ > ωδ, X(ωδ, λ ωδ ) = i) = 1 - π i (ωδ)(I - B r )U where, π i (ωδ) = (0, …, 0, 1, 0, …, 0) is a row vector containing 1×(M + 1)N elements, where the (ω(M + 1)+i)-th element is 1 and the rest are 0.

2. The adaptive maintenance method for mechanical equipment facing dynamic working conditions according to claim 1, characterized in that, When the conditional reliability level of the device is higher than the warning threshold, a long interval Δ is adopted 1 ; When the conditional reliability level of the device is lower than the warning threshold, the monitoring interval becomes smaller to Δ 2 , and the monitoring frequency of the device increases; When the equipment condition reliability returns above the warning threshold again, the monitoring interval changes from Δ 2 back to Δ 1 ; when the equipment conditional reliability level is lower than the maintenance threshold of the equipment, preventive maintenance is carried out on the equipment; when the equipment fails, failure replacement is carried out on the equipment.

3. The adaptive maintenance method for mechanical equipment facing dynamic working conditions according to claim 2, characterized in that, assuming that the change of the working conditions follows a normal distribution, there are two failure modes for the mechanical equipment to be maintained, namely soft failure and hard failure; Soft failure means that the degradation value of the mechanical equipment exceeds the preset failure threshold; When the mechanical equipment fails randomly due to factors such as external impact and hidden manufacturing defects, the failure mode of the equipment is hard failure.

4. The adaptive maintenance method for mechanical equipment facing dynamic working conditions according to claim 3, characterized in that, Select the drift parameter as the random factor to represent the influence of the dynamic working conditions; When the degradation value exceeds the preset failure threshold, the equipment will have a soft failure; the mathematical expression of this Wiener process is: X(t,λ t ) = X(0) + λ t t + σB(t) where X(0) and σ are both constants, B(t) is a standard Brownian process, and λ t is a random factor representing dynamic working conditions, and its distribution follows a normal distribution; The parameters Θ=(μ λ ,σ λ 2 ,σ) of the degradation model can be solved by the maximum likelihood estimation algorithm; The system hard failure rate is represented by the proportional hazards model, and its covariates are represented by the Wiener process with a random factor to represent the influence of mechanical equipment degradation on the failure rate, and its mathematical expression is: where h 0 (t) is the baseline hazard function at time t, and the Weibull distribution is adopted, that is, h 0 (t) = βt β-1 / α β , γ is the regression parameter, which only depends on the degradation value X(t, λ t ).

5. The adaptive maintenance method for mechanical equipment facing dynamic working conditions according to claim 4, characterized in that, For any monitoring interval [(k - 1)Δ, kΔ], where k ∈ N, the degradation amount of the mechanical equipment is independently and identically distributed and follows a normal distribution, that is, X(kΔ, λ kΔ ) - X((k - 1)Δ, λ (k-1)Δ ) ~ N(λΔ, σ 2 Δ).

6. The adaptive maintenance method for mechanical equipment facing dynamic working conditions according to claim 5, characterized in that, Achieve the minimum operation and maintenance cost per unit time. According to renewal theory, this problem is equivalent to finding the optimal control strategy such that: where CC and CL respectively represent the total operation and maintenance cost and the time length of the equipment in one cycle, and the maintenance strategy uses an algorithm based on the semi-Markov decision process to solve the optimal control threshold and monitoring interval.

7. The adaptive maintenance method for mechanical equipment facing dynamic working conditions according to claim 4, characterized in that, The specific operation process of the semi-Markov decision is as follows: First, determine the state space of the SMDP. Divide the range of the conditional reliability [0, 1] into K equal parts, W 1 ,W 2 ∈{1, 2, …, K}; Assume that at the n 1 +n 2 -th sampling, the conditional reliability of the device is greater than W 1 , then it is defined as the state (i, n 1 +n 2 ). The state set of this state is S 1 ={(i, n 1 +n 2 ): R(i, n 1 Δ 1 +n 2 Δ 2 ) > W 1}, where the first element represents the degradation state value of the device, that is The second element represents the sampling times; Similarly, S 2 ={(j, n 1 + n 2 ): W 2 < R(j, n 1 Δ 1 + n 2 Δ 2 ) ≤ W 1} represents the state set where the equipment condition reliability is between two thresholds. In particular, when i, j = M, that is, when a soft failure of the equipment occurs, the equipment is replaced due to failure; when the equipment condition reliability is lower than the warning threshold, the equipment undergoes preventive maintenance, defined as S 3 ={PM}; when the equipment fails, that is, a hard failure occurs, the equipment is in the failure state S 4 ={F}, and failure replacement should be carried out; both preventive maintenance and failure replacement will return the equipment to the brand-new state S 0 ={(0, 0)}; therefore, the state space of the SMDP is defined as S = S 0 ∪ S 1 ∪ S 2 ∪ S 3 ∪ S 4 ; Secondly, define and calculate three elements in the SMDP, namely, transition probability, expected sojourn time, and expected cost: P r,k : The probability that the current device is in state r ∈ S and will transition to state k ∈ S at the next decision-making moment; τ r : The expected sojourn time of the device in state r ∈ S from the current decision-making moment to the next decision-making moment; C r : The expected cost from the current decision-making moment to the next decision-making moment when the device is in state r ∈ S; Finally, for a given control strategy the operation and maintenance cost of the device can be obtained by the following linear equation: V j = 0, for any state, j ∈ S.

8. The system of the adaptive maintenance method for mechanical equipment facing dynamic working conditions according to any one of claims 1-7, characterized in that, it includes: a degradation modeling module for dynamic working condition equipment, which establishes a degradation model based on the historical maintenance data of the mechanical equipment to be maintained, and selects a random factor from the degradation model to represent the change process of the dynamic working condition; a prediction and update module for conditional reliability, which collects the state monitoring data of the mechanical equipment to be maintained, calculates the health assessment index reflecting the equipment health information by using the rectangular approximation method, takes it as the conditional reliability, and updates it according to the change of the state monitoring interval; and an adaptive maintenance decision-making module, in which a warning threshold W of conditional reliability is pre-stored 1 and a maintenance threshold W 2 , W 1 >W 2 , and different monitoring intervals are selected according to the current conditional reliability.

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