CN111008661B - Croston-XGboost prediction method for reserve demand of aircraft engine - Google Patents

Croston-XGboost prediction method for reserve demand of aircraft engine Download PDF

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CN111008661B
CN111008661B CN201911227124.2A CN201911227124A CN111008661B CN 111008661 B CN111008661 B CN 111008661B CN 201911227124 A CN201911227124 A CN 201911227124A CN 111008661 B CN111008661 B CN 111008661B
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林琳
刘杰
郭丰
吕彦诚
郭昊
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Harbin Institute of Technology
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Abstract

The invention discloses a Croston-XGboost prediction method for a reserve demand of an aero-engine, and relates to a reserve demand prediction method for an aero-engine. The method aims to solve the problem that the prediction accuracy of the existing method for the standby requirement of the aircraft engine is low. The process is as follows: converting an intermittent type primary observation sequence of a backup demand into a backup demand interval sequence and a backup demand sequence based on a Croston method; step two, constructing an XGboost model; step three, establishing a backup demand interval prediction model and a demand quantity prediction model based on the step one and the step two; and step four, predicting deviation from a total cost index based on the backup demand interval prediction model and the backup demand prediction model obtained in the step three. The method is used for the field of prediction of the reserve demand of the aero-engine.

Description

Croston-XGboost prediction method for reserve demand of aircraft engine
Technical Field
The invention relates to a method for predicting reserve demand of an aircraft engine.
Background
The aircraft engine is the main power source and bleed device of aircraft such as civil aviation aircraft. When an aircraft engine requires servicing, it is generally necessary to replace the removed serviced engine with a spare engine. The shortage of backup and launch directly affects the utilization of the aircraft. Meanwhile, the aero-engine is typical high-cost equipment, and if the reserve sending requirement of the fleet can be accurately estimated, support can be provided for optimization of operation and maintenance strategies of the fleet. Therefore, backup demand forecasting has always been a major concern for airlines. In the field of spare part demand prediction, the crossbar method is regarded as a basic method for discontinuous demand prediction, and the crossbar method and the improvement method thereof are widely applied to discontinuous spare part demand prediction. The traditional discontinuous spare part demand prediction method has the problem of low prediction precision, and the prediction precision of the spare part demand of the aero-engine is difficult to meet. Meanwhile, as the aircraft engine belongs to equipment with high reliability, a large number of samples of the backup and distribution requirements are difficult to obtain in a limited-scale fleet.
Disclosure of Invention
The invention aims to solve the problem that the accuracy of predicting the standby demand of an aero-engine is low in the existing method, and provides a Croston-XGboost prediction method for the standby demand of the aero-engine.
The first embodiment is as follows: the Croston-XGboost prediction method for the reserve demand of the aero-engine of the embodiment comprises the following specific processes:
converting an intermittent type primary observation sequence of a backup demand into a backup demand interval sequence and a backup demand sequence based on a Croston method;
step two, constructing an XGboost model;
step three, establishing a backup demand interval prediction model and a demand quantity prediction model based on the step one and the step two;
and step four, predicting deviation from a total cost index based on the backup demand interval prediction model and the backup demand prediction model obtained in the step three.
The invention has the beneficial effects that:
the invention provides a Croston-XGboost reserve demand prediction method in a Croston method framework by using an eXtreme Gradient Boosting (XGboost) model suitable for small sample prediction. Aiming at the characteristic of a small sample of the reserve demand of an aeroengine, a Croston-XGboost reserve demand prediction method is provided. Most of the reserve demand of the aero-engine is intermittent demand, and the reserve demand is difficult to predict directly by a traditional prediction method, so that a Croston framework is adopted to decompose an intermittent reserve demand sequence into a demand sequence and a demand interval sequence. And then, predicting the backup demand and the demand interval by using an XGboost method suitable for small samples. The method for predicting and evaluating the intermittent standby demand is provided by combining the operation and maintenance characteristics of the aero-engine, and the accuracy of predicting the standby demand of the aero-engine is improved. The provided Croston-XGboost prediction method is verified by using actual operation and maintenance data of a certain fleet, and a traditional Croston method, a feedback neural network under a Croston frame, a support vector machine and a gradient descent tree are used as comparison test methods. The Croston-XGboost prediction method achieves a good prediction effect.
The prediction accuracy of a Croston-XGboost standby demand prediction model is compared, a conventional Croston method is used as a reference comparison experiment method in a standby demand prediction comparison experiment, and meanwhile, a conventional feedback Neural Network (BPNN), a Support Vector Machine (SVM) and a GBDT are used as comparison experiment methods in a Croston framework. The reserve capacity and demand interval prediction errors of five groups of comparison experiments including a Croston-XGboost reserve demand prediction model are respectively as follows:
in the prediction error of the reserve demand, the Croston model AAE is 0.302885, the ARE is 0.241987 and the RMSE is 0.631695; in the prediction error of the reserve demand, the BPNN model has the AAE of 0.139423, the ARE of 0.073718 and the RMSE of 0.398314; in the prediction error of the reserve demand, the SVM model AAE is 0.125, the ARE is 0.059295, and the RMSE is 0.379777; in the prediction error of the reserve demand, the GBDT model AAE is 0.125, the ARE is 0.059295, and the RMSE is 0.379777; in the prediction error of the reserve demand, the XGboost model AAE is 0.1875, the ARE is 0.125, and the RMSE is 0.443977;
in the prediction error of the interval of the backup demand, the Croston model AAE is 205.4952, the ARE is 51.91482 and the RMSE is 2241.142; in the prediction error of the backup demand interval, the BPNN model has the AAE of 11.0673, the ARE of 3.1664 and the RMSE of 14.7166; in the prediction error of the backup demand interval, the SVM model AAE is 24.54327, the ARE is 7.408056 and the RMSE is 26.75683; in the prediction error of the backup demand interval, the GBDT model AAE is 11.23558, the ARE is 3.167198 and the RMSE is 15.94266; in the backup demand interval prediction error, an XGboost model AAE is 10.13461, an ARE is 2.774511, and an RMSE is 14.58265;
it can be seen that the XGboost method obtains the best prediction precision in backup demand interval prediction. Meanwhile, because the backup sample size is limited, in a prediction experiment, the average value of 10 prediction results of the BPNN method is taken as a final prediction result. In the backup demand prediction, the prediction accuracy of the SVM method and the BPNN method is better than that of the XGboost method, but the BPNN method still has larger prediction fluctuation.
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FIG. 1 is a flow chart of the present invention.
Detailed Description
The first embodiment is as follows: the Croston-XGboost prediction method for the reserve demand of the aero-engine of the embodiment comprises the following specific processes:
converting an intermittent type primary observation sequence of a backup demand into a backup demand interval sequence and a backup demand sequence based on a Croston method;
step two, constructing an XGboost model;
step three, establishing a backup demand interval prediction model and a demand quantity prediction model (Croston-XGboost backup demand prediction model) based on the step one and the step two;
and step four, predicting deviation from a total cost index based on the backup demand interval prediction model and the backup demand prediction model obtained in the step three.
The second embodiment is as follows: the difference between the first embodiment and the first embodiment is that in the first step, an intermittent type primary observation sequence of the standby power demand is converted into a standby power demand interval sequence and a standby power demand sequence based on a Croston method; the specific process is as follows:
according to the characteristics of spare part requirements, the spare part requirements can be divided into continuous requirements and discontinuous requirements. The intermittent spare part requirement is characterized in that: spare part demand raw observation sequence is mixed with a large number of '0' demand samples. If the non-zero occurrence demand is defined as the spare part demand response, the intermittent spare part demand characteristic can be expressed as that the interval between two adjacent spare part demand responses is larger than the observation time unit of the spare part demand according to the judgment standard provided by Syntetos, and if the average occurrence interval of a certain spare part demand response is 1.32 times of the observation time unit, the spare part demand is the intermittent demand.
Aiming at the characteristic of intermittent spare part requirement, Croston provides a feasible solution, and converts an intermittent original observation sequence of the spare part requirement into a spare part requirement interval sequence and a spare part requirement sequence;
the original observation sequence of the discontinuous type reserve hair requirement is expressed as follows:
Z＝{d0,0,...,0,d1,0,...,0,di,0,...,0,dn} (1)
wherein d isiExpressed as the demand of the ith demand response, diIs a positive integer.
The standby demand interval is defined as an observation interval of two adjacent demand responses; for example, two adjacent demand responses diAnd di+1Between is xi+1A "0" value is required, then diAnd di+1The sequence of the required intervals between is calculated by the formula (2):
yi+1＝xi+1+1 (2)
based on the method, the discontinuous original observation sequence with the formula (1) can be decomposed into a demand interval sequence and a demand sequence, which are respectively expressed as a formula (3) and a formula (4):
Y＝δ(Z)＝{y1,...,yi,…,yn} (3)
D＝γ(Z)＝{d0,d1,...,di,...,dn} (4)
wherein D represents a demand sequence, and Y represents a demand interval sequence; delta and gamma respectively represent the conversion function of the demand interval sequence and the demand quantity sequence, Z is the original observation sequence of the discontinuous type reserve demand, y1For the 1 st demand interval, yiFor the ith demand interval, ynFor the nth demand interval, d0To the initial demand, d11 st demand, diIs the ith demand, dnIs the nth demand.
Demand response d due to demand observation range limitation0The previous demand and the demand interval are not available, and d is predicted0Are discarded.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the second embodiment is different from the first embodiment or the second embodiment in that an XGBoost model is constructed in the second step; the specific process is as follows:
in the demand and demand interval prediction model, the XGBoost model is expressed as:
Figure BDA0002302560690000041
where F represents a function space in which all trees are combined, { F1,f2,…,fKExpressing K regression trees to be solved by the XGboost model,
Figure BDA0002302560690000042
representing the predicted value of sample i; x is the number ofiDenotes yiOr di；
When the prediction model is trained, the minimum loss function is generally used as an optimization target. The loss function of the XGboost method simultaneously comprises a prediction error term and a regularization term, and the prediction accuracy and the generalization of the model can be considered simultaneously in the model training process. The penalty function for the XGboost model is written as:
Figure BDA0002302560690000043
wherein,
Figure BDA0002302560690000044
predict error, y, for sample iiAnd
Figure BDA0002302560690000045
respectively an actual value and a predicted value of the sample i; omega (f)t) The regularization term of the t-th regression tree is used for penalizing the complex model and preventing the model from generating an overfitting phenomenon, and can be expressed as:
Figure BDA0002302560690000046
wherein T represents the number of leaf nodes of the tth regression tree, omega represents the weight of all the leaf nodes of the tth regression tree, and gamma is the coefficient of the leaf node, so that XGboost is equivalent to pre-pruning while optimizing the objective function; λ is L2Penalty of regularizationThe coefficients are also to act to prevent overfitting; the prediction value of sample i is expressed in the form of equation (8), and the loss function is expressed in the form of equation (9):
Figure BDA0002302560690000051
Figure BDA0002302560690000052
wherein,
Figure BDA0002302560690000053
for the predicted values of sample i at t trees,
Figure BDA0002302560690000054
is the predicted value of sample i in the existing t-1 trees, ftTo minimize the loss function of the regression tree based on the existing t-1 trees, ft(xi) For the value of sample i in the t-th optimal regression tree, Ω (f)t) Complexity of the t-th optimal regression tree;
for loss function L(t)With taylor expansion, the loss function is expressed in the form of equation (10):
Figure BDA0002302560690000055
wherein, giAnd hiIs an intermediate variable; giAnd hiSpecifically, the formula (11) and the formula (12);
removing constant term (
Figure BDA0002302560690000056
Now the t-th tree is optimized, since the first t-1 trees have already been optimized, only the t-th tree is changing, the first t-1 trees are in a fixed structure, so the numerical value is fixed, the real constant) loss function is expressed in the form of equation (13):
Figure BDA0002302560690000057
Figure BDA0002302560690000058
Figure BDA0002302560690000059
wherein,
Figure BDA00023025606900000510
is the first derivative of the current error function,
Figure BDA00023025606900000511
is the second derivative of the current error function;
will Ij＝{i|q(xi) J is defined as the jth leaf node, then
Figure BDA00023025606900000512
Represented by formula (14):
Figure BDA0002302560690000061
wherein q (x)i) Calculating a function for the leaf node, and calculating the leaf node to which the sample i belongs; omegajRepresenting the jth leaf node weight of the tth regression tree;
to solve the minimum of the loss function, the two ends of equation (14) are differentiated to obtain ωjOf (2) an optimal solution
Figure BDA0002302560690000062
As shown in formula (15); by using
Figure BDA0002302560690000063
Calculating the loss function to obtain the formula (16):
Figure BDA0002302560690000064
Figure BDA0002302560690000065
in the XGboost method, a greedy algorithm is adopted to segment the existing leaf nodes. In order to limit the growth of the decision tree, when the gain is larger than the threshold value gamma, node segmentation is performed. Since γ is a coefficient of a leaf node in the regular term, optimization is performed with the minimum loss function as a target, which is equivalent to performing pre-pruning on the decision tree. In view of the above optimization process, compared with the traditional neural network model, the XGBoost can be better applied to the prediction problem of small samples. Meanwhile, the XGboost method can utilize a central processing unit of a computer to perform multi-thread parallel computation, and compared with the traditional GBDT algorithm, the XGboost method has the advantage that the computation efficiency and the precision are greatly improved.
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the embodiment is different from the first to the third embodiment in that a backup demand interval prediction model and a demand quantity prediction model (crossbar-XGBoost backup demand prediction model) are established in the third step based on the first step and the second step; the specific process is as follows:
the backup requirement of the aircraft engine meets the characteristic of discontinuous requirement. According to the invention, the original observation value of the reserve demand is decomposed into a reserve demand sequence and a demand interval sequence under a Croston framework. Because the prediction of the reserve demand of the aircraft engine has the characteristic of small sample size, the invention adopts the XGboost method suitable for small sample prediction to establish a reserve demand prediction model and a demand interval prediction model.
Through the analysis of the actual operation and maintenance conditions of the aircraft engine, the reserve demand of the fleet is directly influenced by the state of the fleet. For example, when the fleet is large in size and the average self-renewal cycle of the engine is high, the fleet backup demand interval is short and the backup demand is large. Therefore, the proposed backup demand prediction model takes into account fleet status as well. When the reserve demand and the demand interval are predicted, the main state parameters of the fleet are used as covariates of a prediction model. The flow chart of the proposed aircraft engine fleet reserve demand prediction model based on the Croston-XGboost method is shown in FIG. 1.
Backup demand interval prediction model Oy＝{Oy1,Oy2,...,Oyn}；
Backup demand prediction model Od＝{Od1,Od2,...,Odn}。
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the difference between this embodiment and one of the first to fourth embodiments is that, in the fourth step, based on the backup demand interval prediction model and the backup demand prediction model obtained in the third step, the prediction deviates from the total cost index; the specific process is as follows:
although conventional prediction error characterization, such as: the Mean Absolute Error (MAE), the Mean Relative Error (MRE), and the Root Mean Square Error (RMSE) can be used to estimate the prediction accuracy of the prediction model. However, in discontinuous demand prediction, the characteristics of discontinuous demands are not considered in the traditional prediction error characterization method. The intermittent reserve power demand prediction evaluation method is provided according to intermittent demand characteristics and by considering the actual operation and maintenance conditions of an aircraft fleet of an aircraft engine.
In the actual operation and maintenance of the aircraft engine, when the aircraft engine needs to be disassembled for maintenance, in order to ensure the utilization rate of the aircraft, a spare engine is required to replace the disassembled engine, namely, a spare demand response is generated. The backup demand response may consume a corresponding amount of the backup engine. Therefore, in the proposed discontinuous backup demand prediction evaluation method, it is assumed that the fleet prepares a backup according to the model prediction result. And when the prediction result deviates from the actual reserve demand, expressing the prediction deviation as a deviation cost index, and evaluating the prediction precision of the model by using the deviation cost index.
Considering the actual operation and maintenance characteristics of the aircraft engine, firstly, the inventory cost rate and the renting cost rate in the deviation cost index are defined. Inventory costs are incurred when the predicted backup response is ahead of the actual backup response, or the predicted backup demand is greater than the actual backup demand. In combination with the actual operation and maintenance conditions of the aircraft engine, the inventory cost can be understood as: the fleet prepares the backup according to the prediction result, but the backup response does not consume the prepared backup, so the backup allowance generates inventory cost. When the predicted backup response is delayed compared with the actual backup response, or the predicted backup amount is smaller than the actual backup demand amount, the lease cost is generated. In combination with the actual operation and maintenance conditions of the aircraft engine, the renting cost can be understood as: the backup transmission prepared according to the prediction result is not enough to meet the actual backup transmission response, the actual backup transmission requirement needs to be met in a renting backup transmission mode, and corresponding renting cost is generated.
In summary, in the proposed discontinuous backup demand prediction evaluation method, the prediction deviates from the total cost index:
Figure BDA0002302560690000081
wherein, CiA predicted cost deviation index representing a sample i;
Figure BDA0002302560690000082
wherein, yi,predAnd yi,realRespectively representing a predicted value and an actual value of the demand interval; di,predAnd di,realRespectively representing a predicted value and an actual value of the demand; c. CrentAnd cownRespectively representing the renting cost rate and the inventory cost rate; c'rentAnd c'ownRespectively representing the rent sending amount deviation rate and the stock deviation rate; n represents the total number of prediction samples, and i represents the prediction sample number.
Other steps and parameters are the same as in one of the first to fourth embodiments.
The following examples were used to demonstrate the beneficial effects of the present invention:
the first embodiment is as follows:
and (3) a stand-by demand prediction comparison experiment of the fleet:
in order to verify a Croston-XGboost aircraft engine reserve demand prediction model. Operation and maintenance data of a sample fleet from 2007 to 2016 are collected, a reserve demand daily observation sequence is used as a reserve demand original observation sequence, and the reserve demand of the sample fleet is a typical intermittent demand according to an intermittent spare part demand discrimination standard.
According to the Croston method framework, the original observation sequence of the reserve demand is decomposed into a reserve demand sequence and a demand interval sequence. And decomposing the original observation sequence of the reserve demand of the sample fleet to obtain 213 data of the reserve demand and the demand interval. Namely: the standby demand sequence is formed by arranging 213 standby demand data according to a demand response time sequence, and the standby demand interval sequence is formed by corresponding 213 standby demand interval data. In a backup demand prediction experiment, a backup demand sequence and a demand interval sequence obtained by decomposition are used as sample data.
In order to fully utilize limited reserve demand samples, a reserve demand prediction experiment is performed in a sequential prediction mode. And (3) sequential testing: the method comprises the steps that standby demand samples are arranged according to a demand response time sequence, when the first m samples are used for a demand prediction experiment, the first (m-1) samples serve as training samples, and the mth sample serves as a test sample. In the prediction experiment of the standby requirement, the minimum number of training samples is set to be 5, and 213 pairs of standby requirement samples of a sample fleet are converted into 208 groups of training test sets. In the backup demand prediction comparison experiment, all machine learning methods adopt a sequential testing mode.
The state of the fleet is considered in the proposed Croston-XGboost backup demand prediction model. And the demand prediction experiment collects the state information of the fleet when the sample fleet is subjected to the secondary reserve demand response, and the state information of the fleet is used as a covariate for reserve demand quantity prediction and reserve demand interval prediction. The fleet status information utilized includes: total number of on-wing engines; a total flight cycle at the wing engine; average flight cycle at the wing engine; total number of engines under repair; repairing the engine for a total flight cycle; mean flight cycle at the repair engine; total number of available engines; available engine total flight cycles; the average flight cycle of the engine can be used.
In the XGboost prediction model, RMSE is used as a training error evaluation parameter, the depth of a maximum decision tree is set to be 8 layers, the learning rate is set to be 0.1, and the number of maximum estimators is set to be 800. The predicted backup demand amount and backup demand interval are shown in table 1.
TABLE 1 example backup demand and demand Interval prediction results
Figure BDA0002302560690000091
In order to compare the prediction accuracy of the Croston-XGboost standby demand prediction model, a conventional Croston method is used as a reference comparison experiment method in the standby demand prediction comparison experiment, and meanwhile, a conventional feedback Neural Network (BPNN), a Support Vector Machine (SVM) and a GBDT are used as comparison experiment methods in a Croston framework. The reserve capacity and demand interval prediction errors of five groups of comparative experiments including the Croston-XGboost reserve demand prediction model are shown in tables 2 and 3 respectively.
TABLE 2 Reserve demand prediction error
Figure BDA0002302560690000092
TABLE 3 backup demand Interval prediction error
Figure BDA0002302560690000101
From the two tables, the XGboost method obtains the best prediction precision in backup demand interval prediction. Meanwhile, because the backup sample size is limited, in a prediction experiment, the average value of 10 prediction results of the BPNN method is taken as a final prediction result. In the backup demand prediction, the prediction accuracy of the SVM method and the BPNN method is better than that of the XGboost method, but the BPNN method still has larger prediction fluctuation.
In order to evaluate the interval type reserve power demand prediction more comprehensively, in a reserve power demand prediction comparison experiment, comprehensive evaluation is carried out on each group of reserve power prediction models by using the discontinuous reserve power demand prediction evaluation method provided by the text. And the comprehensive evaluation takes the total cost index as an evaluation index. The associated cost ratio is set as: c. Crent＝50；cown＝20；c′rent＝100 and c′own150. The prediction bias total cost index of each prediction model is shown in table 4.
TABLE 4 Total cost estimate by comparative experimental prediction
Figure BDA0002302560690000102
It is clear from the above table that the proposed crossbar-XGBoost backup demand prediction model obtains the smallest prediction bias total cost index. Compared with other four comparative experiment methods, the Croston-XGboost reserve demand prediction model has better comprehensive prediction performance and can provide basic support for the actual operation and maintenance of the aircraft engine fleet.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.

Claims (2)

1. The Croston-XGboost prediction method for the reserve demand of the aircraft engine is characterized by comprising the following steps of: the method comprises the following specific processes:
converting an intermittent type primary observation sequence of a backup demand into a backup demand interval sequence and a backup demand sequence based on a Croston method; the specific process is as follows:
converting an intermittent standby transmission demand original observation sequence into a standby transmission demand interval sequence and a standby transmission demand sequence;
the original observation sequence of the discontinuous type reserve hair requirement is expressed as follows:
Z＝{d0,0,...,0,d1,0,...,0,di,0,...,0,dn} (1)
wherein d isiExpressed as the demand of the ith demand response, diIs a positive integer;
the standby demand interval is defined as an observation interval of two adjacent demand responses;
two adjacent demand responses diAnd di+1Between is xi+1A "0" value is required, then diAnd di+1The sequence of the required intervals between is calculated by the formula (2):
yi+1＝xi+1+1 (2)
decomposing an intermittent standby transmission demand original observation sequence shown as a formula (1) into a demand interval sequence and a demand sequence, which are respectively expressed as a formula (3) and a formula (4):
Y＝δ(Z)＝{y1,...,yi,…,yn} (3)
D＝γ(Z)＝{d0,d1,...,di,...,dn} (4)
wherein D represents a demand sequence, and Y represents a demand interval sequence; delta and gamma respectively represent the conversion function of the demand interval sequence and the demand quantity sequence, Z is the original observation sequence of the discontinuous type reserve demand, y1For the 1 st demand interval, yiFor the ith demand interval, ynFor the nth demand interval, d0To the initial demand, d11 st demand, diIs the ith demand, dnIs the nth demand;
step two, constructing an XGboost model; the specific process comprises the following steps:
the XGboost model is represented as:
Figure FDA0002809070120000011
where F represents a function space in which all trees are combined, { F1,f2,…,fKExpressing K regression trees to be solved by the XGboost model,
Figure FDA0002809070120000012
representing the predicted value of sample i; x is the number ofiDenotes yiOr di；
The penalty function for the XGboost model is written as:
Figure FDA0002809070120000021
wherein,
Figure FDA0002809070120000022
predict error, y, for sample iiAnd
Figure FDA0002809070120000023
respectively an actual value and a predicted value of the sample i; omega (f)t) The regularization term for the t-th regression tree is expressed as:
Figure FDA0002809070120000024
wherein T represents the leaf node number of the T regression tree, omega represents the weight of all the leaf nodes of the T regression tree, gamma is the coefficient of the leaf node, and lambda is L2A regular penalty factor; the prediction value of sample i is expressed in the form of equation (8), and the loss function is expressed in the form of equation (9):
Figure FDA0002809070120000025
Figure FDA0002809070120000026
wherein,
Figure FDA0002809070120000027
for the predicted values of sample i at t trees,
Figure FDA0002809070120000028
is the predicted value of sample i in the existing t-1 trees, ftTo minimize the loss function of the regression tree based on the existing t-1 trees, ft(xi) For the value of sample i in the t-th optimal regression tree, Ω (f)t) Complexity of the t-th optimal regression tree;
for loss function L(t)With taylor expansion, the loss function is expressed in the form of equation (10):
Figure FDA0002809070120000029
wherein, giAnd hiIs an intermediate variable; giAnd hiSpecifically, the formula (11) and the formula (12);
the loss function of the removal constant term is expressed in the form of equation (13):
Figure FDA00028090701200000210
Figure FDA00028090701200000211
Figure FDA00028090701200000212
wherein,
Figure FDA0002809070120000031
is the first derivative of the current error function,
Figure FDA0002809070120000032
is the second derivative of the current error function;
will Ij＝{i|q(xi) J is defined as the jth leaf node, then
Figure FDA0002809070120000033
Represented by formula (14):
Figure FDA0002809070120000034
wherein q (x)i) Calculating a function for the leaf node, and calculating the leaf node to which the sample i belongs; omegajRepresenting the jth leaf node weight of the tth regression tree;
to solve the minimum of the loss function, the two ends of equation (14) are differentiated to obtain ωjOf (2) an optimal solution
Figure FDA0002809070120000035
As shown in formula (15); by using
Figure FDA0002809070120000036
Calculating the loss function to obtain the formula (16):
Figure FDA0002809070120000037
Figure FDA0002809070120000038
step three, establishing a backup demand interval prediction model and a demand quantity prediction model based on the step one and the step two; the specific process comprises the following steps:
backup demand interval prediction model Oy＝{Oy1,Oy2,…,Oyn}；
Backup demand prediction model Od＝{Od1,Od2,…,Odn}；
And step four, predicting deviation from a total cost index based on the backup demand interval prediction model and the backup demand prediction model obtained in the step three.
2. The Croston-XGboost prediction method for the reserve demand of an aircraft engine according to claim 1, characterized in that: in the fourth step, based on the backup demand interval prediction model and the backup demand prediction model obtained in the third step, the deviation of the prediction from the total cost index is obtained; the specific process is as follows:
prediction deviation from total cost index:
Figure FDA0002809070120000041
wherein, CiA predicted cost deviation index representing a sample i;
Figure FDA0002809070120000042
wherein, yi,predAnd yi,realRespectively representing a predicted value and an actual value of the demand interval; di,predAnd di,realRespectively representing a predicted value and an actual value of the demand; c. CrentAnd cownRespectively representing the renting cost rate and the inventory cost rate; c'rentAnd c'ownRespectively representing the rent sending amount deviation rate and the stock deviation rate; n represents the total number of prediction samples, and i represents the prediction sample number.
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