A method for corrective sequential monitoring and maintenance of equipment facing the impact of random faults, as well as a storage medium and an electronic device

Abstract

The present invention belongs to the technical field related to equipment maintenance, and specifically discloses a corrective sequential monitoring and maintenance method for equipment facing the impact of random failures, as well as a storage medium and an electronic device. The method includes the following steps: 1) Using historical state monitoring data, establish a proportional hazards model (PHM), and predict the remaining useful life (RUL) of the equipment based on the model; 2) Construct a correction factor model based on the error between the predicted value and the true value of the RUL to obtain a corrected RUL predicted value; 3) Taking the corrected RUL under the random failure mode as the control standard, formulate a maintenance strategy with sequential monitoring intervals and decision control limits; 4) Construct an optimization algorithm based on semi-Markov decision process (SMDP), and iteratively obtain the optimal corrected RUL decision control limits and sequential monitoring intervals; (5) Online obtain the state monitoring data of the equipment, and perform high-low frequency monitoring according to the corrected RUL level. The method proposed by the present invention is beneficial to reasonably monitor the operating state of the equipment, can save the equipment operation and maintenance costs, effectively improve the economy of equipment operation, and has strong operability in actual engineering.

Description

Technical Field

[0001] The present invention belongs to the field of equipment maintenance, and particularly relates to a corrective sequential monitoring and maintenance method for equipment facing the impact of random failures, as well as a storage medium and an electronic device. Background Art

[0002] In manufacturing and industrial production, equipment is prone to degradation and failure due to use and aging, which may affect product quality or cause accidental failures, resulting in serious economic losses. Predictive maintenance has received wide attention because it can make full use of various condition monitoring data to provide comprehensive solutions for the health assessment, prediction, and maintenance strategies of complex industrial equipment. In actual engineering, the application of predictive maintenance technology can reasonably avoid impending failures. To avoid downtime losses and high maintenance costs caused by random failures, operation and maintenance technicians should determine an appropriate PM time (preventive maintenance time) according to production needs and specific optimization goals.

[0003] In this field, most of the existing methods adopt a periodic monitoring interval. For cases with high monitoring costs, such methods may not be the best monitoring strategy. On the other hand, one of the main challenges of predictive maintenance is to obtain reliable RUL (Remaining Useful Life) prediction results and apply them to maintenance strategies. However, there is a certain degree of error in the RUL prediction process, resulting in false alarms or missed alarms in the formulated maintenance decisions.

[0004] In summary, the corrective sequential monitoring strategy based on two monitoring intervals should be widely applied in actual engineering due to its strong operability. In addition, for equipment affected by random failures, how to more accurately predict its remaining life and ensure preventive maintenance before the occurrence of failures is an urgent problem to be solved. Summary of the Invention

[0005] Aiming at the problems and deficiencies in the prior art, the purpose of the present invention is to provide a corrective sequential monitoring and maintenance method for equipment facing the impact of random failures, as well as a storage medium and an electronic device.

[0006] To achieve the purpose of the invention, the technical solution adopted by the present invention is as follows:

[0007] The first aspect of the present invention provides a corrective sequential monitoring and maintenance method for equipment facing the impact of random failures, which is characterized by specifically including the following steps:

[0008] (1) According to the historical condition monitoring data of the equipment to be maintained, establish a proportional hazards model PHM to describe the random failure rate of the equipment, and predict the remaining useful life (RUL) of the equipment based on the random failure occurrence model;

[0009] (2) Construct a correction factor model that can reflect the dynamic deviation of the prediction based on the error between the predicted RUL value and the true value, and then combine the RUL obtained in step (1) to obtain the corrected RUL prediction value;

[0010] (3) Use the corrected RUL prediction value under the random failure mode as the control standard, and specify a maintenance strategy with sequential monitoring intervals and decision control limits;

[0011] (4) With the goal of minimizing the long-term expected average cost per unit time, construct a semi-Markov decision process (SMDP) optimization algorithm for the corrected RUL under the random failure mode, and iteratively obtain the optimal corrected RUL decision control limits and sequential monitoring intervals.

[0012] According to the above method, further, the establishment process of the proportional hazard model in step (1) is as follows:

[0013] Use the proportional hazard model PHM to describe the random failure rate of the equipment, and its random failure rate function is expressed as: λ(t) = λ0(t)ψ(θX t )

[0014] Where λ0(t) is the baseline hazard function, and the Weibull distribution is selected to be expressed as λ0(t) = βt β-1 / α β , where t is the service age; α > 0 is the scale parameter; β > 0 is the shape parameter;

[0015] Where ψ(θX t ) is the link function, which is related to the value of the covariate X t and the covariate coefficient θ, and is expressed in the form of an exponential function as ψ(θX t ) = exp(θX t ), and the covariate X t represents the degradation process of the equipment.

[0016] According to the above method, further, use the gamma process to model the degradation process {X t , t ≥ 0} of the equipment, and its probability density function can be expressed as:

[0017]

[0018] Where the shape parameter v(t) and the inverse scale parameter u are both greater than 0, and Γ(v(t)) is the gamma function.

[0019] For the equipment with the degradation state of X t and that has not failed before the service age t, the conditional reliability that it can still operate normally after the service age t + r can be deduced as:

[0020]

[0021] Wherein, r represents the operating time of the device after the in-service age t, and λ0(s) represents the Weibull distribution;

[0022] The expected residence time of the device during the interval [t, t + c) can be expressed by the following formula:

[0023]

[0024] Wherein, c represents the operating time of the device after the in-service age t.

[0025] According to the above method, further, the process of predicting the remaining useful life of the device is as follows: Define the remaining useful life RUL of the device as Y = {y: T_t|T > t, X t}, where the non-negative random variable T represents the random time of device failure. Based on the proportional hazard model PHM, when the current degradation state of the device is X t , the probability density function of the device RUL at time t can be expressed as:

[0026]

[0027] Wherein, the symbol A = α -β exp(θX t ), y represents the random variable of the RUL probability density function, α > 0, is the scale parameter; β > 0, is the shape parameter;

[0028] In addition, according to the above formula, the cumulative distribution function of the random variable Y can be obtained, and its closed-form expression is:

[0029]

[0030] For the device that has not failed before time t, the predicted value result of its RUL can be approximated as:

[0031]

[0032] Wherein w represents the operating time of the device after the in-service age t.

[0033] According to the above method, further, the process of obtaining the corrected RUL predicted value in step (2) is as follows:

[0034] Define the correction factor as:

[0035]

[0036] Wherein, m is the total number of historical data of the target device, represents the true RUL of device ω at time t;

[0037] The beta distribution is used to model the correction factor η, which is expressed as:

[0038]

[0039] where a and b are two positive shape parameters, and B(a, b) is the beta function;

[0040] Define the predicted value of the corrected RUL as Since the variables η and y are independent of each other, their joint probability density function can be expressed as f(η, y) = f η (η)·f Y (y);

[0041] Use the random variable Z = η·Y to represent the predicted value of the corrected RUL. The cumulative distribution function of the random variable Z can be derived as follows:

[0042]

[0043] where y represents the random variable of the RUL probability density function.

[0044] According to the above method, further, the maintenance strategy with sequential monitoring intervals and decision control limits in step (3) is: taking the corrected RUL under the random failure mode as the control standard, formulating a maintenance strategy with sequential monitoring intervals and PM control limit K1 and warning control limit K2, where K1 < K2; when the predicted value of the corrected RUL of the equipment is lower than the warning control limit K2, the monitoring frequency will increase, that is, from the long monitoring interval η1 to the short monitoring interval η2.

[0045] According to the above method, even further, the maintenance strategy with sequential monitoring intervals and decision control limits in step (3) is specifically: for a brand-new equipment or an equipment that can be regarded as brand-new after maintenance, use a longer monitoring interval to conduct condition monitoring on it. When the predicted value of the corrected RUL is higher than K2, continue to maintain long-interval monitoring. When the predicted value of the corrected RUL is between K1 and K2, increase the monitoring frequency of the equipment, that is, use a shorter monitoring interval to conduct condition monitoring. Whether it is long-interval or short-interval monitoring, once the predicted value of the corrected RUL is lower than K1, perform PM measures on the equipment. Random failures may occur during the operation of the system. Whenever a failure of the equipment is found, corrective maintenance measures will be immediately implemented.

[0046] According to the above method, further, in step (4), taking the minimization of the long-term operating expected average cost per unit time as the optimization goal, according to the renewal theory, this problem is equivalent to finding the optimal strategy such that:

[0047]

[0048] where \(g(\xi * )\) represents minimizing the long - term running expected average cost per unit time, \(C_C\) and \(C_L\) respectively represent the running cost and time of the device in one cycle.

[0049] According to the above method, further, the operation process of constructing the SMDP optimization algorithm for correcting the RUL prediction value under the random failure mode in step (4) includes:

[0050] Divide the predicted value of the corrected RUL into \(L\) equal parts, and the interval of each part is where represents the maximum expected life when the degradation state is 0; set the preventive maintenance control limit as \(K_1 = k_1\Delta\), and the warning control limit for the conversion of long and short monitoring intervals as \(K_2 = k_2\Delta\), \(k_1,k_2\in(1,2,\cdots,L)\); define the states of the SMDP as follows:

[0051] State \((L,0)\): The device is in a brand - new state;

[0052] State \((k,n_1)\): When monitoring at the time point \(n_1h_1\), the corrected RUL of the device is in the range of \((k - 1)\Delta\) to \(k\Delta\), \(k\in(0,L)\) and \(k\) is an integer;

[0053] State \((k,n_1 + n_2)\): When monitoring at the time point \(n_1h_1 + n_2h_2\), the corrected RUL of the device is in the range of \((k - 1)\Delta\) to \(k\Delta\), \(k\in(0,L)\) and \(k\) is an integer;

[0054] State \(M\): The predicted value of the corrected RUL of the device is in the range of 0 to \(K_1\), and preventive maintenance measures will be executed; when the total running time exceeds the maximum value \(T\) max ), preventive maintenance measures will also be taken;

[0055] State \(F\): The device is in a failure state, and corrective maintenance measures will be immediately executed;

[0056] Therefore, the state space of the SMDP is defined as: \(\Omega=\Omega_0\cup\Omega_1\cup\Omega_2\cup\Omega_3\cup\Omega_4\), where \(\Omega_0=\{(L,0)\}\), \(\Omega_1=\{(k,n_1)|z > K_2,n_1h_1 < T\) max \}, \(\Omega_2=\{(k,n_1 + n_2)|K_1 < z < K_2,n_1h_1 + n_2h_2 < T\) max \}, \(\Omega_3=\{M\}\), \(\Omega_4=\{F\}\).

[0057] According to the above method, further, the optimization algorithm of the SMDP in step (4) divides the corrected RUL into multiple states in the state space \(\Omega\), and the transition probability \(P\) of each state i，j , the expected sojourn time \(\tau\) i and the expected cost \(C\)i The definitions are as follows:

[0058] P i，j : The probability that the current device is in state i ∈ Ω and transitions to state j ∈ Ω at the next decision-making moment;

[0059] τ i : The expected sojourn time for the device to remain until the next decision-making moment under the condition that the current state is in i ∈ Ω;

[0060] C i : The expected cost for the device to remain until the next decision-making moment under the condition that the current state is in i ∈ Ω;

[0061] According to the above method, further, for a given control policy ξ = {K1, K2, h1, h2}, the long-term operation expected average cost per unit time g(ξ) of the device can be obtained by solving the following system of linear simultaneous equations:

[0062]

[0063] V r = 0, for any state r ∈ Ω.

[0064] The second aspect of the present invention provides an electronic device, including a memory and a processor. A computer program is stored on the memory, and when the processor executes the computer program, it implements the device corrective sequential monitoring and maintenance method for random fault impacts as described in the first aspect of the present invention.

[0065] The third aspect of the present invention provides a computer-readable storage medium, characterized in that a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a computer processor, it implements any step in the device corrective sequential monitoring and maintenance method for random fault impacts as described in the first aspect of the present invention.

[0066] The fourth aspect of the present invention provides a computer program product, including a computer program, characterized in that when the computer program is executed by a processor, it implements any step in the device corrective sequential monitoring and maintenance method for random fault impacts as described in the first aspect of the present invention.

[0067] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0068] The present invention uses a gamma process to describe the degradation process of a device, establishes a PHM to simultaneously combine the service age and degradation state information, and uses it to describe the random failure rate of the device. According to the established PHM, closed-form expressions of the probability density function and cumulative distribution function of the RUL are derived. A correction factor model that can reflect the dynamic deviation of the prediction is constructed based on the error between the predicted value and the true value of the RUL, and then the corrected RUL is obtained. In the SMDP optimization algorithm applicable to the corrected RUL under the random failure mode, the optimal corrected RUL decision control limit and sequential monitoring interval are solved, and monitoring and preventive maintenance are carried out accordingly. The method provided by the present invention is beneficial to reasonably monitor the operation state of the device, can save the operation and maintenance cost of the device, effectively improve the economy of the device operation, and has strong operability in practical engineering. Description of the Drawings

[0069] Figure 1 It is a flowchart of the corrective sequential monitoring and maintenance method for a device facing the influence of random failures provided by the present invention;

[0070] Figure 2 It is a diagram showing the state monitoring data of a group of degradation paths in Embodiment 2 of the present invention;

[0071] Figure 3 It is a flowchart of the corrective sequential monitoring and maintenance strategy in Embodiment 2 of the present invention;

[0072] Figure 4 It is a block diagram of the online decision-making structure in Embodiment 2 of the present invention;

[0073] Figure 5 It is a diagram of the corrective sequential monitoring and maintenance decision-making process of historical data 1 in Embodiment 2 of the present invention;

[0074] Figure 6 It is a diagram of the corrective sequential monitoring and maintenance decision-making process of historical data 2 in Embodiment 2 of the present invention. Detailed Embodiments

[0075] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0076] Embodiment 1

[0077] A corrective sequential monitoring and maintenance method for a device facing the influence of random failures, Figure 1 For the flowchart of the method, it specifically includes the following steps:

[0078] Step 1: Based on the historical status monitoring data of the device to be maintained, establish a proportional hazards model (PHM) to describe the random failure rate of the device, and predict the remaining useful life (RUL) of the device based on the random failure rate model;

[0079] The specific implementation process of Step 1 is as follows:

[0080] (1.1) Since the occurrence of random failures of the device depends not only on the service age but also on its degradation state, in order to more accurately predict the health state of the device, a proportional hazards model (PHM) is used to describe the random failure rate of the device, and its random failure rate function is expressed as:

[0081] λ(t) = λ0(t)ψ(θX t )

[0082] In the formula, λ0(t) is the baseline hazard function, and the Weibull distribution is selected to be expressed as λ0(t) = βt β-1 / α β , where t is the service age; α > 0 is the scale parameter; β > 0 is the shape parameter;

[0083] In the formula, ψ(θX t ) is the link function, which is related to the value of the covariate X t and the covariate coefficient θ, and is expressed in the form of an exponential function as ψ(θX t ) = exp(θX t ), and the covariate X t represents the degradation process of the device;

[0084] (1.2) Use the gamma process to model the degradation process {X t , t ≥ 0} of the device, and its probability density function can be expressed as:

[0085]

[0086] In the formula, the shape parameter v(t) and the inverse scale parameter u are both greater than 0, and Γ(v(t)) is the gamma function.

[0087] Based on the status monitoring data of the target device, the parameter values of the PHM model are obtained by the maximum likelihood estimation method;

[0088] (1.3) For a device with a degradation state of X t and that has not failed before the service age t, the conditional reliability that it can still operate normally after the service age t + r can be deduced as:

[0089]

[0090] Wherein, r represents the operating time of the device after the in-service age t, and λ0(s) represents the Weibull distribution;

[0091] The RUL of the device can be defined as Y = {y: T - t|T > t, X t}, where the non-negative random variable T represents the random time of device failure. Based on the above Weibull distribution λ0(t) = βt β-1 / α β and the exponential function ψ(θX t ) = exp(θX t ) for PHM modeling, under the condition that the current degradation state of the device is X t , the probability density function of the device RUL at time t can be expressed as:

[0092]

[0093] Where the symbol A = α -β exp(θX t ), y represents the random variable of the RUL probability density function, α > 0, is the scale parameter; β > 0, is the shape parameter

[0094] In addition, according to the above formula, the cumulative distribution function of the random variable Y can be obtained, and its closed-form expression can be derived as:

[0095]

[0096] For the device that has not failed before time t, the predicted value result of its RUL can be approximated as:

[0097]

[0098] Where w represents the operating time of the device after the in-service age t.

[0099] Step 2: Construct a correction factor model based on the error between the predicted value and the true value of the RUL, which can reflect the dynamic deviation of the prediction. Then, combined with the RUL obtained in step one, the predicted value of the corrected RUL can be obtained.

[0100] The specific implementation process of step 2 is as follows:

[0101] Define the correction factor as:

[0102]

[0103] Where m is the total number of historical data of the target device, represents the true RUL of device ω at time t. The present invention uses the beta distribution to model η, which is expressed as:

[0104]

[0105] Where a and b are two positive shape parameters, and B(a, b) is the beta function.

[0106] The predicted value of the modified RUL is defined as Since the variables η and y are independent of each other, their joint probability density function can be expressed as f(η, y) = f η (η)·f Y (y). The predicted value of the modified RUL is represented by the random variable Z = η·Y. The cumulative distribution function of the random variable Z can be derived as follows:

[0107]

[0108] Step 3: Using the modified RUL under random failure mode as the control criterion, a maintenance strategy with sequential monitoring intervals and decision control limits is formulated.

[0109] Using the modified RUL under random failure mode as the control standard, a maintenance strategy with sequential monitoring intervals and PM control limits K1 and K2 is developed, where K1 is less than K2. When the equipment's predicted modified RUL falls below the warning control limit K2, the monitoring frequency is increased, changing from a long monitoring interval h1 to a short monitoring interval h2.

[0110] The specific process of this strategy is as follows: For new equipment or equipment that can be considered new after maintenance, condition monitoring is performed at longer monitoring intervals. When the predicted value of the revised RUL exceeds K2, long-interval monitoring is continued. When the predicted value of the revised RUL is between K1 and K2, the monitoring frequency of the equipment is increased, that is, condition monitoring is performed at shorter monitoring intervals. Regardless of whether monitoring is performed at long or short intervals, if the predicted value of the revised RUL falls below K1, PM measures are implemented on the equipment. Random failures may occur during system operation, and corrective maintenance measures are immediately implemented whenever a equipment failure is detected.

[0111] Step 4: Taking minimizing the expected average cost per unit time for long-term operation as the optimization objective, an optimization algorithm of the semi-Markov decision process (SMDP) for the modified RUL under random failure mode is constructed, and the optimal modified RUL decision control limits and sequential monitoring intervals are obtained iteratively.

[0112] The specific implementation process of step 4 is:

[0113] To minimize the expected average cost per unit time in the long run g(ξ * ) is the optimization objective to determine the modified RUL decision control limit and sequential monitoring interval. According to the update theory, this problem is equivalent to finding the optimal control strategy So that:

[0114]

[0115] In the formula, CC and CL respectively represent the operating cost and time of the device in one cycle.

[0116] The specific operation process of constructing the SMDP optimization algorithm for the corrected RUL under the random failure mode is as follows:

[0117] (4.1) First, it is necessary to determine the state space of the SMDP. Divide the predicted value of the corrected RUL into L equal parts, and the interval of each part is where represents the maximum expected life when the degradation state is 0. Set the PM control limit as K1 = k1Δ, and the warning control limit for the conversion of long and short monitoring intervals as K2 = k2Δ, where k1, k2 ∈ (1, 2,..., L). Define the states of the SMDP as follows:

[0118] · State (L, 0): The device is in a brand-new state.

[0119] · State (k, n1): At the time point of n1h1 monitoring, the corrected RUL of the device is in the range of (k - 1)Δ to kΔ, where k ∈ (0, L) and k is an integer.

[0120] · State (k, n1 + n2): At the time point of n1h1 + n2h2 monitoring, the corrected RUL of the device is in the range of (k - 1)Δ to kΔ, where k ∈ (0, L) and k is an integer.

[0121] · State M: The predicted value of the corrected RUL of the device is in the range of 0 to K1, and PM will be executed. When the total operating time exceeds the maximum value T max PM measures will also be taken.

[0122] · State F: The device is in a failed state, and corrective maintenance measures will be immediately executed.

[0123] Therefore, the state space of the SMDP is defined as: Ω = Ω0 ∪ Ω1 ∪ Ω2 ∪ Ω3 ∪ Ω4, where Ω0 = {(L, 0)}, Ω1 = {(k, n1)|z > K2, n1h1 < T max}, Ω2 = {(k, n1 + n2)|K1 < z < K2, n1h1 + n2h2 < T max}, Ω3 = {M}, Ω4 = {F}.

[0124] (4.2) Secondly, define and calculate three elements in the SMDP, the transition probability P i，j , the expected sojourn time τ i and the expected cost C i :

[0125] Pi，j : The probability that the current device is in state \(i\in\Omega\) and will transition to state \(j\in\Omega\) at the next decision-making moment.

[0126] \(\tau\) i : The expected sojourn time for the device to remain until the next decision-making moment, given that the current state is \(i\in\Omega\).

[0127] \(C\) i : The expected cost for the device to remain until the next decision-making moment, given that the current state is \(i\in\Omega\).

[0128] (4.3) Finally, for a given control policy \(\xi=\{K_1, K_2, h_1, h_2\}\), the long-term expected average cost per unit time \(g(\xi)\) of the device can be obtained by solving the following system of linear simultaneous equations:

[0129]

[0130] \(V\) r \( = 0\), for any state \(r\in\Omega\)

[0131] Step 5: Online obtain the state monitoring data of the device, obtain the RUL under the random failure mode, perform high-low frequency monitoring according to the corrected RUL level, and give maintenance decisions.

[0132] Example 2

[0133] A corrective sequential monitoring and maintenance method for devices facing random failure impacts, specifically including the following steps:

[0134] Step 1: In this example, a set of state monitoring data containing 10 degradation paths is selected, as Figure 2 shown. The initial degradation state of the target device is \(X_0 = 0\), and state monitoring information is obtained every 10 hours. Among them, 9 end with observable failures, and the remaining 1 stops monitoring because the maximum operating time is exceeded.

[0135] First, establish a proportional hazards model (PHM) by combining the service age and degradation state information. Its random failure rate function is expressed as: \(\lambda(t)=\lambda_0(t)\psi(\theta X\) t )

[0136] where \(\lambda_0(t)\) is the baseline hazard function, and is represented by the Weibull distribution as \(\lambda_0(t)=\beta t\) β-1 / \(\alpha\) β , where \(\alpha>0\) is the scale parameter; \(\beta>0\) is the shape parameter; \(\psi(\theta X\) t ) is the link function, which is related to the value of the covariate \(X\) t and the covariate coefficient \(\theta\), and is represented in the form of an exponential function as \(\psi(\theta X\) t )=\(\exp(\theta X\)t ), the covariate X t represents the degradation process of the device.

[0137] Secondly, a gamma process is used to model the degradation process {X t , t≥0} of the device, and its probability density function can be expressed as:

[0138]

[0139] where the shape parameter v(t) and the inverse scale parameter u are both greater than 0, and Γ(v(t)) is the gamma function. According to Figure 2 the historical degradation path data shown, the parameter values of the PHM are obtained by the maximum likelihood estimation method as: α = 1848.6, β = 1.193, θ = 0.354, u = 19.53, v(t) = 4.768×10 -2 t.

[0140] Finally, for a device with a degradation state of X t and no failure before the in-service age t, the conditional reliability that the device can still operate normally after the service age t+r can be deduced as:

[0141]

[0142] where r represents the operating time of the device after the in-service age t, and λ0(s) represents the Weibull distribution;

[0143] According to the deduced conditional reliability formula, for a device that has not failed before time t, the prediction result of its RUL can be approximated as:

[0144]

[0145] where w represents the operating time of the device after the in-service age t.

[0146] Step 2:

[0147] Define the correction factor η as:

[0148]

[0149] where m = 10 is the total number of historical data of the target device, represents the true RUL of the device ω at time t.

[0150] The present invention uses a beta distribution to model η, which is expressed as:

[0151]

[0152] where a and b are two positive shape parameters, and B(a, b) is the beta function.

[0153] According to the definition of the correction factor η, the correction factors at different times can be calculated, and then their expected value is statistically obtained as 0.6252 and the variance is 0.0065. Combining with the expected value and variance formulas of the beta distribution, the parameters a = 21.985 and b = 13.177 can be obtained.

[0154] The predicted value of the corrected RUL is defined as Since the variable η and the variable y are independent of each other, their joint probability density function can be expressed as f(η, y) = f η (η)·f Y (y). Let the random variable Z = η·Y represent the predicted value of the corrected RUL. The cumulative distribution function of the random variable Z can be derived as:

[0155]

[0156] Step 3: Develop a corrective sequential monitoring and maintenance strategy for equipment affected by random failures;

[0157] See Figure 3 , the present invention takes the corrected RUL in the random failure mode as the control standard, and develops a maintenance strategy with sequential monitoring intervals and PM control limits K1 and warning control limits K2, where K1 < K2. When the predicted value of the corrected RUL of the equipment is lower than the warning control limit K2, the monitoring frequency will increase, that is, from the long monitoring interval h1 to the short monitoring interval h2.

[0158] Step 4:

[0159] Taking the long-term operating expected average cost g(ξ) per unit time as the optimization objective to determine the optimal decision variable. According to the renewal theory, this problem is equivalent to finding the optimal control strategy such that:

[0160]

[0161] In the formula, CC and CL respectively represent the operating cost and time of the equipment in one cycle;

[0162] The present invention divides the predicted value of the corrected RUL into L = 10 equal parts, and each part has an interval of where the maximum expected life when the degradation state is 0 Set the PM control limit as K1 = k1Δ, and the warning control limit for the conversion of long and short monitoring intervals as K2 = k2Δ, where k1, k2 ∈ (1, 2,..., L). Define the states of the SMDP as follows:

[0163] · State (L, 0): The equipment is in a brand-new state.

[0164] · State (k, n1): When monitored at time point n1h1, the corrected RUL of the device is within the range of (k - 1)Δ to kΔ, where k ∈ (0, L) and k is an integer..

[0165] · State (k, n1 + n2): When monitored at time point n1h1 + n2h2, the corrected RUL of the device is within the range of (k - 1)Δ to kΔ, where k ∈ (0, L) and k is an integer..

[0166] · State M: The predicted value of the corrected RUL of the device is within the range of 0 to K1, and PM will be executed. When the total operating time exceeds the maximum value T max PM measures will also be taken.

[0167] · State F: The device is in a failure state, and corrective maintenance measures will be immediately executed.

[0168] Therefore, the state space of the SMDP is defined as: Ω = Ω0 ∪ Ω1 ∪ Ω2 ∪ Ω3 ∪ Ω4, where Ω0 = {(L, 0)}, Ω1 = {(k, n1)|z > K2, n1h1 < T max}, Ω2 = {(k, n1 + n2)|K1 < z < K2, n1h1 + n2h2 < T max}, Ω3 = {M}, Ω4 = {F}.

[0169] Secondly, define and calculate three elements in the SMDP, the transition probability P i，j 、the expected sojourn time τ i and the expected cost C i ;

[0170] P i，j : The probability that the current device is in state i ∈ Ω and transitions to state j ∈ Ω at the next decision moment.

[0171] τ i : The expected sojourn time for the device to remain until the next decision moment under the condition that the current state is i ∈ Ω.

[0172] C i : The expected cost for the device to remain until the next decision moment under the condition that the current state is i ∈ Ω.

[0173] Using the degradation state corresponding to the midpoint of the interval divided by the SMDP to approximately calculate the transition probability, it can be expressed as:

[0174]

[0175]

[0176]

[0177]

[0178]

[0179]

[0180]

[0181]

[0182] The calculation formula for the expected residence time is as follows:

[0183] τ (L，0) = Λ(X0, 0, h1) + T F [1 - R(X0, 0, h1)]

[0184]

[0185]

[0186]

[0187]

[0188] The calculation formula for the expected cost is as follows:

[0189] C (L，0) = C I ·R(X0, 0, h1) + C F [1 - R(X0, 0, h1)]

[0190]

[0191]

[0192]

[0193]

[0194] Finally, for the given control strategy ξ = {K1, K2, h1, h2}, according to the time and cost parameters: preventive maintenance time T P = 12, corrective maintenance time T F = 24, monitoring cost C I = 150, preventive maintenance cost C P = 2000, corrective maintenance cost C F = 10000, the long - term expected average cost per unit time of the equipment g(ξ) can be obtained by solving the following system of linear simultaneous equations:

[0195]

[0196] V r = 0, for any state r ∈ Ω

[0197] Through iterative calculation, the optimal control strategy is obtained The corresponding minimum long-term operating expected average cost per hour g(ξ * ) = 10.75.

[0198] Step 5

[0199] Online decision-making: Refer to Figure 4 , after obtaining the optimal corrected RUL decision control limit and sequential monitoring interval in the SMDP optimization algorithm for correcting RUL applicable to the stochastic failure mode, the online condition monitoring of the target device can be carried out. After obtaining the current condition monitoring data, the RUL under the stochastic failure mode can be predicted by combining the constructed stochastic failure rate model and dynamic correction factor model. High-low frequency monitoring is carried out according to the corrected RUL level, and maintenance decisions are given.

[0200] 2]This embodiment provides a decision process diagram for the corrective sequential monitoring and maintenance strategy of the device based on two historical condition monitoring data, as shown in Figure 5 and Figure 6 shown, where Figure 5 is the decision process diagram for the corrective sequential monitoring and maintenance of historical data 1, Figure 6 is the decision process diagram for the corrective sequential monitoring and maintenance of historical data 2.

[0201] In Figure 5 , a brand-new device starts running from time 0, and condition monitoring is carried out with a relatively long monitoring interval h1. According to the monitored data, the RUL of the device is predicted using the established PHM and dynamic correction factor. At the 1st and 2nd monitoring times, the predicted values of the corrected RUL are 663.43 and 589.32 respectively, both higher than the warning control limit K2, and the operating condition is good, so the long-interval monitoring should be continued. At the 3rd monitoring time, the predicted value of the corrected RUL is 525.19, which is between the PM control limit K1 and the warning control limit K2, in a warning state, and then a shorter monitoring interval h2 should be used to carry out condition monitoring on the device. At the 8th monitoring time, the predicted value of the corrected RUL is 399.51, lower than the PM control limit K1. Therefore, immediately implement PM measures to avoid serious economic losses caused by the occurrence of stochastic failures.

[0202] In Figure 6Among them, a brand-new device starts running at time 0, and a long monitoring interval h1 is adopted for condition monitoring. According to the data obtained from the monitoring, the RUL of the device is predicted by using the established PHM and dynamic correction factor. At the first monitoring, the predicted value of its corrected RUL is 634.67, which is higher than K2, and the long-interval monitoring is continued. At the second monitoring, the predicted value of its corrected RUL is 537.23, which is lower than K2 and higher than K1. After that, a shorter monitoring interval h2 is adopted to conduct condition monitoring on the device. At the ninth monitoring, the predicted value of its corrected RUL is 421.51, which is lower than K1. At this time, the PM measure should be immediately implemented.

[0203] Using the above technical method, the present invention provides a corrective sequential monitoring and maintenance method for a device affected by random failures, which can model the random failure rate and construct a dynamic correction factor based on historical condition monitoring data. By obtaining the online condition monitoring data of the target device, the RUL under the random failure mode can be obtained, and high-low frequency monitoring is carried out according to the corrected RUL level, and maintenance decisions are given. This method has been verified by algorithms, and the results show that this maintenance method can adopt appropriate monitoring intervals and maintenance measures to prevent the occurrence of failures. While saving the operation and maintenance costs of the device, it also has strong operability.

[0204] Embodiment 3

[0205] A computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, any step in a corrective sequential monitoring and maintenance method for a device affected by random failures as described in Embodiment 1 or 2 is implemented.

[0206] The computer-readable medium described in this application can be a computer-readable signal medium, a computer-readable storage medium, or any combination of the two. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples of a computer-readable storage medium can include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In this application, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. And in this application, a computer-readable signal medium can include a data signal propagated in a baseband or as part of a carrier wave, in which computer-readable program code is carried. Such a propagated data signal can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. A computer-readable signal medium can also be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device. The program code contained on a computer-readable medium can be transmitted using any appropriate medium, including but not limited to: wireless, wire, optical fiber, RF, etc., or any suitable combination of the above.

[0207] Computer program code for performing the operations of this application can be written in one or more programming languages or combinations thereof. The programming languages include object-oriented programming languages such as Java, Smalltalk, C++, and also include conventional procedural programming languages such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, executed as an independent software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computer (for example, by using an Internet service provider to connect through the Internet).

[0208] In addition, this embodiment further provides an electronic device, including a memory and a processor. A computer program is stored on the memory, and when the processor executes the computer program, any step in the device corrective sequential monitoring and maintenance method for random fault impact described in Embodiment 1 or 2 is implemented.

[0209] Furthermore, the process of the device corrective sequential monitoring and maintenance method for random fault impact described in Embodiment 1 or 2 can be implemented as a computer software program. For example, this embodiment includes a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program contains program codes for executing the method. In such an embodiment, the computer program can be downloaded and installed from the network, and / or installed from a removable medium. When the computer program is executed by the processor, the above functions defined in the method of this application are executed.

[0210] The above embodiments are specific implementation manners of the present invention, but the implementation manners of the present invention are not limited by the above embodiments. Any combination, change, modification, substitution, or simplification that does not exceed the design concept of the present invention falls within the protection scope of the present invention.

Claims

1. A corrective sequential monitoring and maintenance method for equipment facing the impact of random faults, characterized in that, Specifically, it includes the following steps: (1) Based on the historical state monitoring data of the equipment to be maintained, establish a proportional hazards model (PHM) to describe the random failure incidence rate of the equipment, and predict the remaining useful life (RUL) of the equipment based on the random failure occurrence model; (2) Construct a correction factor model that can reflect the dynamic deviation of the prediction based on the error between the predicted value and the true value of the RUL, and then combine the RUL obtained in step (1) to obtain the corrected RUL predicted value; (3) Taking the corrected RUL predicted value in the random failure mode as the control standard, formulate a maintenance strategy with sequential monitoring intervals and decision control limits; (4) Taking the minimization of the long-term operating expected average cost per unit time as the optimization objective, construct a semi-Markov decision process (SMDP) optimization algorithm for the corrected RUL in the random failure mode, and iteratively obtain the optimal corrected RUL decision control limits and sequential monitoring intervals; (5) Online obtain the state monitoring data of the equipment, calculate the RUL in the random failure mode, and perform high-low frequency monitoring according to the corrected RUL level; The process of obtaining the corrected RUL predicted value in step (2) is as follows: Define the correction factor as: where m is the total number of historical data of the target device, represents the true RUL of device ω at time t; Use the beta distribution to model the correction factor η, which is expressed as: In the formula, a and b are two positive shape parameters, and B(a, b) is the beta function; Define the predicted value of the corrected RUL as Since the variables η and y are independent of each other, their joint probability density function can be expressed as f(η, y) = f η (η)·f Y (y); Use the random variable \(Z = \eta\cdot Y\) to represent the predicted value of the corrected RUL. The cumulative distribution function of the random variable \(Z\) can be derived as follows: In the formula, y represents the random variable of the RUL probability density function.

2. The method according to claim 1, wherein The establishment process of the proportional hazards model described in step (1) is: use the proportional hazards model (PHM) to describe the random failure incidence rate of the equipment, and its random failure incidence rate function is expressed as: λ(t) = λ0(t)ψ(θX t ) where λ0(t) is the baseline hazard function, and is expressed by the Weibull distribution as λ0(t) = βt β-1 / α β , where t is the service age; α > 0 is the scale parameter; β > 0 is the shape parameter; where ψ(θX t ) is the link function, which is related to the value of the covariate X t and the covariate coefficient θ, and is expressed in the form of an exponential function as ψ(θX t ) = exp(θX t ), and the covariate X t represents the degradation process of the device.

3. The method according to claim 2, characterized in that, The process of predicting the remaining useful life of the equipment is: Define the remaining useful life RUL of the device as Y = {y: T - t|T > t, X t}, where the non - negative random variable T represents the random time of device failure. Based on the proportional hazard model PHM, when the current degradation state of the device is X t , the probability density function of the device RUL at time t can be expressed as: where the symbol A = α -β exp(θX t ), y represents the random variable of the RUL probability density function, α > 0, which is the scale parameter; β > 0, which is the shape parameter; In addition, according to the above formula, the cumulative distribution function of the random variable Y can be obtained, and its closed-form expression is: For the equipment that has not failed before time t, the result of its RUL predicted value can be approximated as: In the formula, w represents the operating time of the equipment after the in-service age t.

4. The method according to claim 3, wherein The maintenance strategy with sequential monitoring intervals and decision control limits described in step (3) is specifically: taking the corrected RUL in the random failure mode as the control standard, formulate a maintenance strategy with sequential monitoring intervals and PM control limit K1 and warning control limit K2, where K1 < K2; when the corrected RUL predicted value of the equipment is lower than the warning control limit K2, the monitoring frequency will increase, that is, from the long monitoring interval h1 to the short monitoring interval h2.

5. The method according to claim 4, characterized in that The operation process of constructing the SMDP optimization algorithm for the corrected RUL predicted value in the random failure mode described in step (4) includes: The predicted value of the corrected RUL is divided into L equal parts, with each part having an interval of where represents the maximum expected life when the degradation state is 0; set the preventive maintenance control limit as K1 = k1Δ, and the warning control limit for the conversion of long and short monitoring intervals as K2 = k2Δ, where k1, k2 ∈ (1, 2,..., L); define the states of the SMDP as follows: State (L, 0): The equipment is in a brand-new state; State (k, n1): At the time point of n1h1 monitoring, the corrected RUL of the equipment is in the range of (k - 1)Δ to kΔ, k ∈ (0, L) and k is an integer; State (k, n1 + n2): At the time point of n1h1 + n2h2 monitoring, the corrected RUL of the equipment is in the range of (k - 1)Δ to kΔ, k ∈ (0, L) and k is an integer; State M: When the predicted value of the corrected RUL of the device is within the range of 0 to K1, preventive maintenance measures will be executed; preventive maintenance measures will also be taken when the total operating time exceeds the maximum value T max ; State F: The equipment is in a failure state, and repair maintenance measures will be immediately executed; Therefore, the state space of SMDP is defined as: Ω = Ω0 ∪ Ω1 ∪ Ω2 ∪ Ω3 ∪ Ω4, where Ω0 = {(L, 0)}, Ω1 = {(k, n1)|z > K2, n1h1 < T max}, Ω2 = {(k, n1 + n2)|K1 < z < K2, n1h1 + n2h2 < T max}, Ω3 = {M}, Ω4 = {F}.

6. The method according to claim 5, wherein For a given control strategy ξ = {K1, K2, h1, h2}, the long-term operating expected average cost per unit time g(ξ) of the equipment can be obtained by solving the following system of linear simultaneous equations: V r = 0, for any state r ∈ Ω..

7. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, any step in the device corrective sequential monitoring and maintenance method for random fault impact as described in any one of claims 1-6 is implemented.

8. A computer-readable storage medium, characterized in that, A computer program is stored on the computer-readable storage medium, and when the computer program is executed by a computer processor, any step in the device corrective sequential monitoring and maintenance method for random fault impact as described in any one of claims 1-6 is implemented.

9. An electronic device, comprising a memory and a processor, wherein a computer program is stored on the memory, characterized in that, When the processor executes the computer program, the device corrective sequential monitoring and maintenance method for random fault impact as described in any one of claims 1-6 is implemented.

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