A predictive maintenance method for aircraft engines based on bootstrapped long short-term memory networks

Abstract

The present invention provides an aircraft engine predictive maintenance method based on a bootstrapped long short-term memory network, comprising: obtaining the operation data of the aircraft engine; based on the operation data, obtaining the remaining life prediction interval using a bootstrapped long short-term memory network; based on the remaining life prediction interval, calculating the maintenance cost rate parameter of the aircraft engine; based on the maintenance cost rate parameter, designing a maintenance cost rate function; based on the maintenance cost rate function, determining the optimal maintenance time of the aircraft engine. The present invention solves the relationship between the safety prediction of the aircraft engine and the maintenance cost rate, can determine the optimal maintenance time of the aircraft engine, ensure the normal operation of the aircraft engine, and reduce the maintenance cost at the same time.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft engine maintenance, and specifically but not limited to, relates to an aircraft engine predictive maintenance method based on a bootstrapped long short-term memory network. Background Art

[0002] Aircraft engines are complex mechanical equipment that are affected by a variety of factors during operation, such as temperature, pressure, and rotation speed, which may cause the engine's performance to deteriorate or even fail. In existing aircraft engine maintenance, maintenance plans are usually determined based on the engine's service life and maintenance history. However, the service life of an aircraft engine is affected by a variety of factors, such as the operating environment, frequency of use, maintenance status, etc., so it is difficult to accurately predict the service life of the engine, and the maintenance history of an aircraft engine can only reflect past maintenance conditions, and cannot predict future failures and maintenance needs. Existing maintenance methods usually involve replacing or overhauling the engine after it reaches its service life, which can cause certain waste and environmental pollution.

[0003] Therefore, regular and irregular inspection, maintenance and repair of aircraft engines can ensure that the engine operates in the best condition, improve the reliability and durability of the engine, and thus ensure flight safety. Regular maintenance refers to periodic inspection and maintenance after the engine has been running for a certain period of time (such as 50 hours, 100 hours, etc.). These regular maintenance and inspections can prevent engine failures, and promptly detect and solve potential problems, thereby extending the service life of the engine. The optimal maintenance time for aircraft engines can not only ensure the reliability and durability of the engine, but also increase the industry's profit margin. Too frequent inspections of aircraft engines will result in excessively high maintenance costs. For aircraft engine maintenance companies, reducing maintenance costs is an important means to improve corporate competitiveness. If the maintenance cost is too high, it may cause the company to miss or simplify some potential problems during the maintenance process, thereby posing a hidden danger to aviation safety. Therefore, reducing the maintenance cost of aircraft engines is also one of the important measures to ensure aviation safety.

[0004] In view of this, it is necessary to provide a new method to solve at least part of the above problems. Summary of the invention

[0005] In response to one or more problems in the prior art, the present invention proposes a predictive maintenance method for aircraft engines based on a bootstrapped long short-term memory network, which solves the relationship between aircraft engine safety prediction and maintenance cost rate, can determine the optimal maintenance time of aircraft engines, ensure the normal operation of aircraft engines, and reduce maintenance costs.

[0006] The technical solution to achieve the purpose of the present invention is:

[0007] A predictive maintenance method for aircraft engines based on a bootstrapped long short-term memory network, comprising:

[0008] S1. Obtaining the operating data of the aircraft engine;

[0009] S2. Based on the operating data, obtaining a remaining life prediction interval using a bootstrapped long short-term memory network;

[0010] S3. Calculating a maintenance cost rate parameter of the aircraft engine based on the remaining life prediction interval;

[0011] S4. Designing a maintenance cost rate function based on the maintenance cost rate parameter;

[0012] S5. Determine the optimal maintenance time of the aircraft engine based on the maintenance cost rate function.

[0013] Furthermore, in the aircraft engine predictive maintenance method based on the bootstrapped long short-term memory network of the present invention, obtaining the operating data of the aircraft engine in S1 includes:

[0014] S11. Install pressure, heat and other sensors on aircraft engines;

[0015] S12. The sensor collects operating data of the aircraft engine for several monitoring cycles.

[0016] Furthermore, in the aircraft engine predictive maintenance method based on the bootstrapped long short-term memory network of the present invention, obtaining the remaining life prediction interval in S2 includes:

[0017] S21, in the historical operation data {x s-h+1 ,x s-h+2 ,...,x s}, extract h samples with replacement, repeat M times, and get M training data sets C1, C2, …, C M , s represents a monitoring period of historical operation data;

[0018] S22, construct M long short-term memory networks, the M long short-term memory networks form bootstrapped long short-term memory networks, and the M long short-term memory networks are based on M training data sets C1, C2, ..., C M Train M remaining life prediction models LSTM 1 (·),LSTM 2 (·),…,LSTM M (·):

[0019]

[0020] in, is the remaining life prediction value of the sth monitoring cycle generated by the mth long short-term memory neural network, m∈[1,M], LSTM m (·) represents the mapping function of the m-th LSTM network;

[0021] S23, using the M prediction models LSTM 1 (·),LSTM 2 (·),…,LSTM M (·) For the online running data {x1,x2,...,x h} Perform remaining life prediction and obtain M remaining life prediction sets

[0022]

[0023] in, The remaining life prediction value of the h-th monitoring cycle generated by the m-th long short-term memory neural network;

[0024] S24, for M remaining life prediction sets Perform cumulative averaging to obtain the point predicted life value of the hth monitoring cycle

[0025]

[0026] S25, point prediction life value based on the hth monitoring cycle The remaining life prediction interval of the hth monitoring cycle is calculated as in:

[0027]

[0028]

[0029] represents the misspecification variance of the bootstrapped LSTM network at the hth monitoring period, represents the variance of the bootstrapped LSTM network error in the hth monitoring period, and α represents the significance level; is the critical value of the standard normal distribution, determined by a confidence level of (1-α) 100%.

[0030] Further, in the aircraft engine predictive maintenance method based on the bootstrapped long short-term memory network of the present invention, the misspecified variance of the bootstrapped long short-term memory network in S24 is Point predicted life value based on the hth monitoring cycle The calculation is as follows:

[0031]

[0032] in, represents the misspecification variance of the bootstrapped LSTM network at the hth monitoring period.

[0033] Furthermore, in the aircraft engine predictive maintenance method based on the bootstrapped long short-term memory network of the present invention, the variance of the bootstrapped long short-term memory network error in S24 is It is calculated through the m+1th long short-term memory network, specifically:

[0034]

[0035] Among them, LSTM m+1 (·) represents the mapping function of the m+1th LSTM network; the training input of the m+1th LSTM network is the operating data of the aircraft engine from s-h+1 to s monitoring period in the training set {x s-h+1 ,x s-h+2 ,...,x s}; The training output of the m+1th LSTM network is f s represents the true value of the remaining life in the sth monitoring period in the training set, Represents the predicted value of the remaining life of the s-th monitoring cycle in the training set.

[0036] Furthermore, in the aircraft engine predictive maintenance method based on the bootstrapped long short-term memory network of the present invention, the aircraft engine maintenance cost rate parameter calculated in S3 includes:

[0037] S31, based on the remaining life prediction interval of the hth monitoring cycle Calculate the position parameter μ of the current monitoring period h h :

[0038]

[0039] in, represents the lower bound of the remaining life prediction interval, Represents the upper limit of the remaining life prediction interval;

[0040] S32, based on the remaining life prediction interval of the hth monitoring cycle and the position parameter μ h , calculate the scale parameter σ describing the variance distribution h :

[0041]

[0042] Among them, α is the significance level; t represents the monitoring time.

[0043] Furthermore, in the aircraft engine predictive maintenance method based on the bootstrapped long short-term memory network of the present invention, the maintenance cost rate function in S4 is:

[0044]

[0045] in, Denotes the monitoring time t m =(h+k)ΔT maintenance cost rate, t m =(h+k)ΔT represents the monitoring time of future period k based on the current monitoring period h, ΔT represents the monitoring interval, P(·) represents the probability, C c C is the cost of corrective maintenance caused by sudden failure of aircraft engine. p T is the preventive maintenance cost associated with fixed installation costs, replacement material costs, labor costs, and production losses during maintenance. f is the failure time of the aircraft engine, RUL h Indicates the actual remaining life of the aircraft engine in the current monitoring period h; μ h represents the position parameter; σ h Represents the scale parameter.

[0046] Furthermore, in the aircraft engine predictive maintenance method based on the bootstrapped long short-term memory network of the present invention, the optimal maintenance time of the aircraft engine in S5 is:

[0047]

[0048] in, represents the optimal maintenance time of aircraft engines, It represents the maintenance cost rate at the monitoring time hΔT, where h is the current monitoring period.

[0049] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0050] 1. The aircraft engine predictive maintenance method based on the bootstrapped long short-term memory network of the present invention solves the relationship between aircraft engine safety prediction and maintenance cost rate, which is of great significance for improving enterprise competitiveness, increasing profits, promoting enterprise development and ensuring aviation safety.

[0051] 2. The aircraft engine predictive maintenance method based on the bootstrapped long short-term memory network of the present invention can more effectively capture patterns and trends in time series data and improve the ability to accurately predict the remaining life of aircraft engines.

[0052] 3. The aircraft engine predictive maintenance method based on the bootstrapped long short-term memory network of the present invention can better reflect the uncertainty of the system because it provides a range rather than a single point prediction, which is particularly important for aircraft engine maintenance decisions in complex dynamic environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The accompanying drawings are used to provide a further understanding of the present invention and are used together with the description to explain the embodiments of the present invention, but do not constitute a limitation of the present invention. In the accompanying drawings:

[0054] Figure 1 A flow chart of the aircraft engine predictive maintenance method based on the bootstrapped long short-term memory network of the present invention is shown;

[0055] Figure 2 A schematic diagram showing the remaining life prediction interval of 100 test engines according to an embodiment of the present invention is shown;

[0056] Figure 3 A schematic diagram of the remaining life distribution results constructed for some test samples according to an embodiment of the present invention is shown;

[0057] Figure 4 The figure shows the expected maintenance cost rates of some test samples under different preventive and restorative cost structure scenarios according to an embodiment of the present invention. DETAILED DESCRIPTION

[0058] In order to further understand the present invention, preferred embodiments of the present invention are described below in conjunction with examples. However, it should be understood that these descriptions are only for further illustrating the features and advantages of the present invention, rather than limiting the claims of the present invention.

[0059] The description in this section is only for typical embodiments, and the present invention is not limited to the scope of the embodiments. The combination of different embodiments, the mutual replacement of some technical features in different embodiments, and the mutual replacement of the same or similar prior art means with some technical features in the embodiments are also within the scope of the description and protection of the present invention.

[0060] According to one aspect of the present invention, a method for predictive maintenance of an aircraft engine based on a bootstrapped long short-term memory network is provided. Figure 1 As shown, including:

[0061] S1. Obtaining the operating data of the aircraft engine.

[0062] S11. Install pressure, heat and other sensors on aircraft engines;

[0063] S12. The sensor collects operating data of the aircraft engine for several monitoring cycles.

[0064] S2. Based on the operating data, a bootstrapped long short-term memory network is used to obtain a remaining life prediction interval.

[0065] S21, in the historical operation data {x s-h+1 ,x s-h+2 ,...,x s}, extract h samples with replacement, repeat M times, and get M training data sets C1, C2, …, C M , s represents a monitoring period of historical operation data;

[0066] S22, construct M long short-term memory networks, the M long short-term memory networks form bootstrapped long short-term memory networks, and the M long short-term memory networks are based on M training data sets C1, C2, ..., C M Train M remaining life prediction models LSTM 1 (·),LSTM 2 (·),...,LSTM M (·):

[0067]

[0068] in, is the remaining life prediction value of the sth monitoring cycle generated by the mth long short-term memory neural network, m∈[1,M], LSTM m (·) represents the mapping function of the m-th LSTM network;

[0069] S23, using the M prediction models LSTM 1 (·),LSTM 2 (·),…,LSTM M (·) For the online running data {x1,x2,...,x h} Perform remaining life prediction and obtain M remaining life prediction sets

[0070]

[0071] in, The remaining life prediction value of the h-th monitoring cycle generated by the m-th long short-term memory neural network;

[0072] S24, for M remaining life prediction sets Perform cumulative averaging to obtain the point predicted life value of the hth monitoring cycle

[0073]

[0074] S25, point prediction life value based on the hth monitoring cycle The remaining life prediction interval of the hth monitoring cycle is calculated as in:

[0075]

[0076]

[0077] represents the misspecification variance of the bootstrapped LSTM network at the hth monitoring period, represents the variance of the bootstrapped LSTM network error in the hth monitoring period, and α represents the significance level; is the critical value of the standard normal distribution, determined by the confidence level (1-α) 100%. Where:

[0078] (1) Misspecification variance of bootstrapped LSTM networks Point predicted life value based on the hth monitoring cycle The calculation is as follows:

[0079]

[0080] (2) Variance of bootstrapped LSTM network errors It is calculated through the m+1th long short-term memory network, specifically:

[0081]

[0082] Among them, LSTM m+1 (·) represents the mapping function of the m+1th LSTM network; the training input of the m+1th LSTM network is the operating data of the aircraft engine from s-h+1 to s monitoring period in the training set {x s-h+1 ,x s-h+2 ,...,x s}; The training output of the m+1th LSTM network is f s represents the true value of the remaining life in the s-th monitoring period in the training set, Represents the predicted value of the remaining life of the s-th monitoring cycle in the training set.

[0083] S3. Calculate the maintenance cost rate parameter of the aircraft engine based on the remaining life prediction interval.

[0084] S31, based on the remaining life prediction interval of the hth monitoring cycle Calculate the position parameter μ of the current monitoring period h h :

[0085]

[0086] in, represents the lower bound of the remaining life prediction interval, Represents the upper limit of the remaining life prediction interval;

[0087] S32, based on the remaining life prediction interval of the hth monitoring cycle and the position parameter μ h , calculate the scale parameter σ describing the variance distribution h :

[0088]

[0089] Among them, α is the significance level; t represents the monitoring time.

[0090] S4. Based on the maintenance cost rate parameter, a maintenance cost rate function is designed as follows:

[0091]

[0092] in, Denotes the monitoring time t m =(h+k)ΔT maintenance cost rate, t m =(h+k)ΔT represents the monitoring time of future period k based on the current monitoring period h, ΔT represents the monitoring interval, P(·) represents the probability, C c C is the cost of corrective maintenance caused by sudden failure of aircraft engine. p T is the preventive maintenance cost associated with fixed installation costs, replacement material costs, labor costs, and production losses during maintenance. f is the failure time of the aircraft engine, RUL h Indicates the actual remaining life of the aircraft engine in the current monitoring period h; μ h represents the position parameter; σ h Represents the scale parameter.

[0093] S5. Based on the maintenance cost rate function, determine the optimal maintenance time of the aircraft engine as:

[0094]

[0095] in, represents the optimal maintenance time of aircraft engines, It represents the maintenance cost rate at the monitoring time hΔT, where h is the current monitoring period.

[0096] Example 1

[0097] In order to verify the performance of the aircraft engine predictive maintenance method based on the bootstrapped long short-term memory network proposed in the present invention, the method is implemented on the turbofan engine public degradation data set provided by NASA. The remaining life prediction interval is obtained by using the 100 sets of complete time series from the start of operation to the end of the failure contained in the "train_FD001.txt" file in the data set, and then the maintenance cost rate function is calculated, and finally the optimal maintenance time is obtained.

[0098] like Figure 2 The figure shows the remaining life prediction interval constructed based on the data contained in the "train_FD001.txt" file in the dataset based on the bootstrapped long short-term memory network at a 95% confidence level. The upper and lower bounds of the remaining life prediction interval are then substituted into formula (7) to calculate the maintenance cost rate function parameter μ. h , then μ h Substituting into formula (8), we can get the maintenance cost rate function parameter σ h For example, for the test engine #9, based on the bootstrapped LSTM network, the remaining life prediction interval can be obtained as [89.25, 148.09]. Substituting the upper and lower bounds of the remaining life prediction interval into formula (7), the parameter μ can be calculated. h The value of is 118.67. Next, h =118.67 Substituting into formula (8), we can solve for parameter σ h The value of is 15.01. Similarly, the remaining life distribution parameters of all test engines can be calculated, thereby determining the remaining life probability distribution.

[0099] Table 1 gives the results of some test samples on the normal distribution location parameter μ. h and the scale parameter σ h The first column of Table 1 shows the numbers of some of the selected test engines, the second column shows the actual remaining life of the test engines, and the third column shows the numbers from Figure 2 The last two columns represent the normal distribution and parameters calculated based on the prediction intervals in the third column.

[0100] Table 1 Calculation results of some test engines for the Gaussian distribution position parameter μ and scale parameter σ

[0101]

[0102] As an illustration, Figure 3 The remaining life distribution results constructed for some test samples are shown as an example (test engine #9, test engine #39). Since the mathematical expectation of the remaining life distribution is the position parameter μ h The value of μ hThe value can be regarded as a point estimate of the remaining life. As can be seen from the figure, for test engine #9, the remaining life point estimate is very close to the actual remaining life; while for test engine #39, although the remaining life point estimate deviates from the actual remaining life to a certain extent, the actual remaining life is still within the 95% prediction interval of the constructed remaining life distribution. Although the remaining life point estimate deviates far from the actual remaining life, the actual remaining life can still be surrounded by the 95% prediction interval of the constructed remaining life distribution. The above results show that the constructed remaining life distribution is effective and can describe the uncertainty in the life prediction process. In addition, the remaining life distribution curve constructed for test engine #9 is relatively flat, while the remaining life distribution curve constructed for test engine #39 is thin and tall. This is mainly because the scale parameter σ of test engine #39 h The calculated values ​​are 13.89, which is less than the scale parameter σ of test engine #9. h Calculated value: 15.01.

[0103] After obtaining the remaining life distribution, the maintenance cost function can be constructed by linking the maintenance-related costs, and then the time to implement predictive maintenance can be obtained. When the remaining life prediction is perfect, then the ideal predictive maintenance activity can be planned for an inspection cycle before the system fails. For imperfect remaining life prediction, in various scenarios of corrective and preventive cost structures (C c / C p ), the optimal maintenance time has different planning strategies. Figure 4 As shown in Figure 2, in order to study the applicability of the optimal predictive maintenance strategy, three scenarios of corrective and preventive cost structures are given: C c / C p =1.2, C c / C p =1.5 and C c / C p =2(C p =100). It should be pointed out that:

[0104] 1. Corrective maintenance costs are more expensive than predictive maintenance costs, i.e. C c >C p ;

[0105] 2. Assuming that the engine is inspected every 5 flight cycles, this means that the planned maintenance activity will be at a time in the future that is a multiple of 5 flight cycles;

[0106] 3. The time with the minimum maintenance cost rate is planned as the predicted maintenance time.

[0107] The following is an example of test engine #9, whose actual failure time is T f=166. For test engine #9, when C c / C p =1.2, the expected maintenance cost rate decreases with the increase of engine service time before the 165th flight cycle; and increases slightly with the increase of engine service time after the 165th flight cycle.

[0108] This can be explained in two ways:

[0109] 1. Implementing early maintenance may reduce uptime and increase maintenance cost rate;

[0110] 2. There is a risk of system degradation and failure in the later stage of engine operation, and the maintenance cost rate will also increase.

[0111] Therefore, since the 165th flight cycle has the minimum maintenance cost rate, it can be considered as the appropriate time to perform predictive maintenance. c / C p =1.5 and C c / C p = 2, the predicted maintenance time with the minimum maintenance cost rate is the 155th and 150th flight cycles respectively. This is because when the corrective maintenance cost is much higher than the preventive maintenance cost, the proposed maintenance strategy recommends scheduling predictive maintenance activities as soon as possible to prevent expensive corrective maintenance costs caused by engine failure.

[0112] The description and application of the present invention here are illustrative, and it is not intended to limit the scope of the present invention to the above-mentioned embodiments. The effects or advantages involved in the specification may not be reflected in the actual experimental examples due to the uncertainty of specific condition parameters or other factors, and the effects or advantages are not used to limit the scope of the invention. The deformation and change of the embodiments disclosed here are possible, and the replacement of the embodiments and the various equivalent parts are well known to those of ordinary skill in the art. It should be clear to those skilled in the art that the present invention can be implemented in other forms, structures, arrangements, proportions, and with other components, materials and parts without departing from the spirit or essential features of the present invention. Other deformations and changes can be made to the embodiments disclosed here without departing from the scope and spirit of the present invention.

Claims

1. A method for predictive maintenance of aircraft engines based on bootstrapped long short-term memory networks, characterized in that: include: S1. Obtaining the operating data of the aircraft engine; S2. Based on the operating data, obtaining a remaining life prediction interval using a bootstrapped long short-term memory network; Specifically include: S21, in the historical operation data {x s-h+1 ,x s-h+2 ,…,x s }, extract h samples with replacement, repeat M times, and get M training data sets C1, C2, …, C M , s represents a monitoring period of historical operation data; S22, construct M long short-term memory networks, the M long short-term memory networks form bootstrapped long short-term memory networks, and the M long short-term memory networks are based on M training data sets C1, C2, ..., C M Train M remaining life prediction models LSTM 1 (·),LSTM 2 (·),…,LSTM M (·): in, is the remaining life prediction value of the sth monitoring cycle generated by the mth long short-term memory neural network, m∈[1,M], LSTM m (·) represents the mapping function of the m-th LSTM network; S23, using the M prediction models LSTM 1 (·),LSTM 2 (·),...,LSTM M (·) For the online running data {x g-h+1 ,x g-h+2 ,...,x g } Perform remaining life prediction and obtain M remaining life prediction sets in, The predicted value of remaining life for the g-th monitoring period generated by the m-th LSTM neural network; S24, for M remaining life prediction sets Perform cumulative averaging to obtain the point predicted life value of the g-th monitoring period S25, point prediction life value based on the g-th monitoring cycle The remaining life prediction interval of the g-th monitoring period is calculated as in: represents the estimated variance of the bootstrapped LSTM network at the g-th monitoring period, represents the variance of the bootstrapped LSTM network error in the g-th monitoring period, and α represents the significance level; is the critical value of the standard normal distribution, determined by the confidence level (1-α) 100%; Estimated variance Point predicted life value based on the g-th monitoring cycle The calculation is as follows: in, represents the estimated variance of the bootstrapped LSTM network at the g-th monitoring period; variance It is calculated through the m+1th long short-term memory network, specifically: Among them, LSTM m+1 (·) represents the mapping function of the m+1th LSTM network; the training input of the m+1th LSTM network is the operating data of the aircraft engine from s-h+1 to s monitoring period in the training set {x s-h+1 ,x s-h+2 ,...,x s }; The training output of the m+1th LSTM network is max f s represents the true value of the remaining life in the sth monitoring period in the training set, represents the predicted value of the remaining life in the sth monitoring period in the training set; S3. Calculating a maintenance cost rate parameter of the aircraft engine based on the remaining life prediction interval; S4. Designing a maintenance cost rate function based on the maintenance cost rate parameter; S5. Determine the optimal maintenance time of the aircraft engine based on the maintenance cost rate function.

2. The method for predictive maintenance of aircraft engines based on bootstrapped long short-term memory networks according to claim 1, characterized in that: The operating data of aircraft engines obtained in S1 include: S11. Install pressure sensors and thermal sensors on aircraft engines; S12. The sensor collects operating data of the aircraft engine for several monitoring cycles.

3. The method for predictive maintenance of aircraft engines based on bootstrapped long short-term memory networks according to claim 1, characterized in that: The parameters for calculating the maintenance cost rate of aircraft engines in S3 include: S31, based on the remaining life prediction interval of the g-th monitoring cycle Calculate the position parameter μ of the current monitoring period g g : in, represents the lower bound of the remaining life prediction interval, Represents the upper limit of the remaining life prediction interval; S32, based on the remaining life prediction interval of the g-th monitoring cycle and the position parameter μ g , calculate the scale parameter σ describing the variance distribution g : Among them, α is the significance level; t represents the monitoring time.

4. The method for predictive maintenance of aircraft engines based on bootstrapped long short-term memory networks according to claim 1, characterized in that: The maintenance cost rate function in S4 is: in, Denotes the monitoring time t m =(g+k)ΔT maintenance cost rate, t m =(g+k)ΔT represents the monitoring time of future period k based on the current monitoring period g, ΔT represents the monitoring interval, P(·) represents the probability, C c C is the cost of corrective maintenance caused by sudden failure of aircraft engines. p T is the preventive maintenance cost associated with fixed installation costs, replacement material costs, labor costs, and production losses during maintenance. f is the failure time of the aircraft engine, RUL g represents the actual remaining life of the aircraft engine in the current monitoring period g; μ g represents the position parameter; σ g Represents the scale parameter.

5. The method for predictive maintenance of aircraft engines based on bootstrapped long short-term memory networks according to claim 1, characterized in that: The optimal maintenance time for aircraft engines in S5 is: in, represents the optimal maintenance time of aircraft engines, It represents the maintenance cost rate at the monitoring time gΔT, where g is the current monitoring period.

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