CN111008661B - Croston-XGBoost forecasting method for aero-engine spare power demand - Google Patents

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 Forecasting Method for Aero-engine Spare Demand

technical field

The invention relates to a method for predicting the spare power demand of aero-engines.

Background technique

Aero-engine is the main power source and bleed air device of civil aircraft and other aircraft. When the aircraft engine needs to be repaired, a spare engine is generally required to replace the engine that has been removed and repaired. The shortage of spare engines directly affects the utilization of aircraft. At the same time, aero-engines are typical equipment with high cost of ownership. If the fleet reserve demand can be estimated more accurately, it can provide support for the optimization of fleet operation and maintenance strategies. Therefore, the forecast of spare demand has always been a key concern of airlines. In the field of spare parts demand forecasting, the Croston method is regarded as the basic method of intermittent demand forecasting, and the Croston method and its improved methods are widely used in intermittent spare parts demand forecasting. The traditional intermittent spare parts demand forecasting method has the problem of low forecasting accuracy, and it is difficult to meet the forecasting accuracy of aero-engine spare parts demand. At the same time, because aero-engines are highly reliable equipment, it is difficult to obtain a large number of spare demand samples in a limited-scale fleet.

SUMMARY OF THE INVENTION

The purpose of the present invention is to propose a Croston-XGBoost forecasting method for the spare demand of aero-engines in order to solve the problem of low accuracy in predicting the spare demand of aero-engines by the existing methods.

Specific embodiment 1: The specific process of the Croston-XGBoost prediction method for the aero-engine standby demand in this embodiment is as follows:

Step 1. Convert the original observation sequence of intermittent standby demand into standby demand interval sequence and standby demand sequence based on the Croston method;

Step 2. Build the XGBoost model;

Step 3. Based on Step 1 and Step 2, establish a demand interval forecast model and a demand forecast model for standby delivery;

Step 4: Predict the deviation from the total cost index based on the interval forecasting model of the standby demand and the forecasting model of the standby demand obtained in the third step.

The beneficial effects of the present invention are:

The present invention uses an extreme gradient boosting model (eXtreme GradientBoosting, XGBoost) suitable for small sample prediction, and proposes a Croston-XGBoost standby demand forecasting method under the framework of the Croston method. Aiming at the small sample characteristics of aero-engine spare demand, a Croston-XGBoost spare demand forecasting method is proposed. Most of the aero-engine standby demand is intermittent demand, and it is difficult to predict it directly by traditional forecasting methods. Therefore, the Croston framework is used to decompose the intermittent standby demand sequence into a demand sequence and a demand interval sequence. Furthermore, the XGBoost method suitable for small samples is used to forecast the demand for spares and the demand interval. Combined with the characteristics of aero-engine operation and maintenance, a forecasting and evaluation method for intermittent standby demand is proposed, which improves the forecasting accuracy of aero-engine standby demand. The proposed Croston-XGBoost prediction method is verified by the actual operation and maintenance data of a certain fleet, and the traditional Croston method, feedback neural network under the Croston framework, support vector machine and gradient descent tree are used as comparative test methods. Croston-XGBoost prediction method has achieved good prediction results.

Comparing the prediction accuracy of the Croston-XGBoost standby demand forecasting model, the standby demand forecasting comparison experiment uses the traditional Croston method as the benchmark to compare the experimental methods. At the same time, under the Croston framework, the traditional Back Propagation Neural Network (BPNN), Vector machine (Support Vector Machine, SVM), GBDT as comparative experimental methods. The forecast errors of spare power and demand interval of five sets of comparative experiments including the Croston-XGBoost spare demand forecasting model are as follows:

In the forecast error of standby demand, the Croston model AAE is 0.302885, ARE is 0.241987, and RMSE is 0.631695; in the forecast error of standby demand, the BPNN model AAE is 0.139423, ARE is 0.073718, and RMSE is 0.398314; the forecast error of standby demand is 0.398314; Among them, the AAE of the SVM model is 0.125, the ARE is 0.059295, and the RMSE is 0.379777; in the forecast error of the standby demand, the AAE of the GBDT model is 0.125, the ARE is 0.059295, and the RMSE is 0.379777; in the forecast error of the standby demand, the AAE of the XGBoost model is 0.1875, ARE is 0.125, RMSE is 0.443977;

In the prediction error of the standby demand interval, the Croston model AAE is 205.4952, the ARE is 51.91482, and the RMSE is 2241.142; in the standby demand interval prediction error, the BPNN model AAE is 11.0673, the ARE is 3.1664, and the RMSE is 14.7166; the standby demand interval prediction error is 14.7166; Among them, the AAE of the SVM model is 24.54327, the ARE is 7.408056, and the RMSE is 26.75683; in the forecast error of the standby demand interval, the AAE of the GBDT model is 11.23558, the ARE is 3.167198, and the RMSE is 15.94266; in the forecast error of the standby demand interval, the AAE of the XGBoost model is 10.13461, ARE is 2.774511, RMSE is 14.58265;

It can be seen that the XGBoost method obtains the best prediction accuracy in the forecast of spare demand interval. At the same time, due to the limited number of prepared samples, in the prediction experiment, the average of 10 prediction results of the BPNN method is taken as the final prediction result. In the forecasting of spare demand, the prediction accuracy of SVM method and BPNN method is better than that of XGBoost method, but the BPNN method still has a large prediction fluctuation.

Description of drawings

Fig. 1 is a flow chart of the present invention.

Detailed ways

Specific embodiment 1: The specific process of the Croston-XGBoost prediction method for the aero-engine standby demand in this embodiment is as follows:

Step 1. Convert the original observation sequence of intermittent standby demand into standby demand interval sequence and standby demand sequence based on the Croston method;

Step 2. Build the XGBoost model;

Step 3, based on Step 1 and Step 2, establish a demand interval forecast model and a demand forecast model (Croston-XGBoost standby demand forecast model);

Step 4: Predict the deviation from the total cost index based on the interval forecasting model of the standby demand and the forecasting model of the standby demand obtained in the third step.

Embodiment 2: The difference between this embodiment and Embodiment 1 is that in step 1, the original observation sequence of intermittent standby demand is converted into a standby demand interval sequence and a standby demand sequence based on the Croston method; the specific process for:

According to the characteristics of spare parts demand, spare parts demand can be divided into continuous demand and intermittent demand. The characteristic of intermittent spare parts demand is that a large number of "0" demand samples are mixed in the original observation sequence of spare parts demand. If the occurrence of non-zero demand is defined as the demand response of spare parts, the intermittent demand for spare parts can be expressed as the interval between two adjacent spare parts demand responses is greater than the observation time unit of the demand for spare parts. When the average occurrence interval is 1.32 times the observation time unit, the demand for spare parts is intermittent demand.

In view of the characteristics of intermittent spare parts demand, Croston proposed a feasible solution, which is to convert the original observation sequence of intermittent standby demand into the interval sequence of standby demand and the sequence of standby demand;

The original observation sequence of intermittent standby demand is expressed as:

Z={d ₀ ,0,...,0,d ₁ ,0,...,0,d _i ,0,...,0,d _n } (1)

Among them, d _i represents the demand quantity of the i-th demand response, and d _i is a positive integer.

The standby demand interval is defined as the observation interval of two adjacent demand responses; for example, if there are x _i+1 "0" value demands between two adjacent demand responses d _i and d _i+1 , then d _i and d The demand interval sequence between _i+1 is calculated by formula (2):

y _i+1 = x _i+1 +1 (2)

Based on the above method, the original observation sequence of intermittent standby demand in the form of formula (1) can be decomposed into a demand interval sequence and a demand quantity sequence, which are expressed as formula (3) and formula (4) respectively:

Y=δ(Z)={y ₁ ,...,y _i ,...,y _n } (3)

D=γ(Z)={d ₀ ,d ₁ ,...,d _i ,...,d _n } (4)

Among them, D is the demand sequence, Y is the demand interval sequence; δ(*) and γ(*) are the conversion function functions of the demand interval sequence and the demand sequence, respectively, Z is the original observation sequence of intermittent standby demand, y ₁ is the first demand interval, y _i is the i-th demand interval, _yn is the n-th demand interval, d ₀ is the initial demand, d ₁ is the first demand, d _i is the i-th demand, d _n is the nth demand.

Due to the limited scope of demand observation, the demand and demand interval before the demand response d ₀ cannot be obtained, and d ₀ is discarded in the forecast.

Other steps and parameters are the same as in the first embodiment.

Embodiment 3: The difference between this embodiment and Embodiment 1 or 2 is that the XGBoost model is constructed in the second step; the specific process is:

In the demand quantity and demand interval forecast model, the XGBoost model is expressed as:

表示样本i的预测值；x_i表示y_i或d_i；Among them, F represents the function space composed of all trees, {f ₁ ,f ₂ ,...,f _K } represents the K regression trees to be obtained by the XGBoost model,

represents the predicted value of sample i; x _i represents y _i or d _i ;

When training a prediction model, the optimization goal is generally to minimize the loss function. The loss function of the XGBoost method includes both the prediction error term and the regularization term, which can consider both the prediction accuracy and the generalization of the model during the model training process. The loss function of the XGBoost model is written as:

为样本i预测误差，y_i和

分别为样本i的实际值和预测值；Ω(f_t)为第t棵回归树的正则项，用来惩罚复杂模型，防止模型产生过拟合现象，其可表示为：in,

prediction error for sample i, y _i and

are the actual value and predicted value of sample i, respectively; Ω(f _t ) is the regular term of the t-th regression tree, which is used to punish the complex model and prevent the model from overfitting. It can be expressed as:

Among them, T represents the number of leaf nodes of the t-th regression tree, ω represents the weight of all leaf nodes of the t-th regression tree, and γ is the coefficient of the leaf node, so that XGBoost is equivalent to pre-pruning while optimizing the objective function; λ is the penalty coefficient of L ₂ regularity to prevent over-fitting; the predicted value of sample i is expressed in the form of formula (8), and the loss function is expressed in the form of formula (9):

为样本i在t棵树的预测值，

为样本i在现有的t-1棵树的预测值，f_t为在现有的t-1棵树的基础上，使得损失函数最小的那棵回归树，f_t(x_i)为样本i在第t棵最优回归树的值，Ω(f_t)为第t棵最优回归树的复杂度；in,

is the predicted value of sample i in t trees,

is the predicted value of sample i in the existing t-1 tree, f _t is the regression tree with the smallest loss function based on the existing t-1 tree, f _t ( _xi ) is the sample The value of i in the t-th optimal regression tree, Ω(f _t ) is the complexity of the t-th optimal regression tree;

Taylor expansion of the loss function L ^(t) , the loss function is expressed in the form of equation (10):

Among them, _gi and _hi are intermediate variables; _gi and _hi are specifically expressed as formula (11) and formula (12);

因为前t-1棵树已经优化完成，现在优化第t棵树，只有第t棵树是在变化的，前t-1棵树为固定结构，因此数值固定，实常数)的损失函数表示为式(13)的形式：remove the constant term (

Because the first t-1 tree has been optimized, now optimize the t-th tree, only the t-th tree is changing, the first t-1 tree is a fixed structure, so the value is fixed, real constant) The loss function is expressed as The form of formula (13):

为当前误差函数的一阶导数，

为当前误差函数的二阶导数；in,

is the first derivative of the current error function,

is the second derivative of the current error function;

表示为式(14)：Define I _j ={i|q( _xi )=j} as the jth leaf node, then

Expressed as formula (14):

Among them, q(x _i ) is the leaf node calculation function, which calculates the leaf node to which the sample i belongs; ω _j represents the weight of the jth leaf node of the tth regression tree;

如式(15)所示；利用

对损失函数进行计算，即得到式(16)：In order to find the minimum value of the loss function, the two ends of equation (14) are derived to obtain the optimal solution of ω _j

As shown in formula (15); using

Calculate the loss function to get equation (16):

In the XGBoost method, a greedy algorithm is used to segment the existing leaf nodes. In order to limit the growth of the decision tree, when the gain is greater than the threshold γ, node segmentation is performed. Since γ is also the coefficient of the leaf node in the regular term, optimizing with the goal of minimizing the loss function is equivalent to pre-pruning the decision tree. In view of the above optimization process, compared with the traditional neural network model, XGBoost can be better applied to the prediction problem of small samples. At the same time, the XGBoost method can use the computer central processing unit to perform multi-threaded parallel computing. Compared with the traditional GBDT algorithm, the computing efficiency and accuracy of XGBoost are greatly improved.

Other steps and parameters are the same as in the first or second embodiment.

Embodiment 4: The difference between this embodiment and one of Embodiments 1 to 3 is that in the step 3, the interval forecasting model for standby demand and the demand forecast model (Croston-XGBoost standby demand) are established based on steps 1 and 2. prediction model); the specific process is:

Because the spare engine demand of aero-engines meets the characteristics of intermittent demand. The invention decomposes the original observation value of the standby demand into the standby demand sequence and the demand interval sequence under the Croston framework. Due to the characteristics of a small sample size in the forecasting of aero-engine standby demand, the present invention adopts the XGBoost method suitable for small sample forecasting to establish a standby demand forecasting model and a demand interval forecasting model.

After analyzing the actual operation and maintenance of aero-engines, the fleet standby demand is directly affected by the fleet status. For example, when the fleet size is large and the average engine recycle cycle is high, the fleet spare demand interval is shorter and the spare engine demand is larger. Therefore, the proposed spare demand forecasting model also considers the fleet status. The main state parameters of the fleet are used as covariates of the forecasting model when forecasting the spare demand and demand interval. The flowchart of the proposed aero-engine fleet standby demand forecasting model based on the Croston-XGBoost method is shown in Figure 1.

Prediction model for the interval of standby demand O _y ={O _y1 ,O _y2 ,...,O _yn };

The demand forecasting model O _d ={O _d1 ,O _d2 ,...,O _dn }.

Other steps and parameters are the same as one of the first to third embodiments.

Embodiment 5: The difference between this embodiment and one of Embodiments 1 to 4 is that in the step 4, based on the standby demand interval prediction model and the standby demand forecast model obtained in the step 3, the prediction deviates from the total cost index; The specific process is:

Although traditional prediction error characterizations, such as mean absolute error (MAE), mean relative error (MRE), and root mean squared error (RMSE), can be used to evaluate the performance of prediction models. prediction accuracy. But in intermittent demand forecasting, the traditional prediction error characterization method does not take into account the characteristics of intermittent demand. According to the characteristics of intermittent demand and considering the actual operation and maintenance of aero-engine fleets, this paper proposes a forecasting and evaluation method for intermittent standby engine demand.

In the actual operation and maintenance of aero-engines, when the on-wing engine needs to be dismantled and repaired, in order to ensure the utilization rate of the aircraft, it is necessary to replace the dismantled engine with a spare engine, that is, a spare engine demand response is generated. Standby demand response consumes a corresponding number of spare engines. Therefore, in the proposed evaluation method of intermittent standby demand forecasting, it is assumed that the fleet is ready for standby according to the model prediction results. When the forecast result deviates from the actual standby demand, the forecast deviation is expressed as a deviation cost index, and the deviation cost index is used to evaluate the prediction accuracy of the model.

Considering the actual operation and maintenance characteristics of aero-engines, the inventory cost rate and rental cost rate in the deviation cost index are first defined. Inventory costs will be incurred when the predicted standby response is earlier than the actual standby response, or the predicted standby demand is larger than the actual standby demand. Combined with the actual operation and maintenance of aero-engines, the inventory cost can be understood as: the fleet prepares spare engines according to the forecast results, but the actual spare engine response does not consume the prepared spare engines, and the spare engine reserve will generate inventory costs. When the predicted standby response is delayed compared with the actual standby response, or the predicted standby demand is smaller than the actual standby demand, the rental cost will be incurred. Combined with the actual operation and maintenance of aero-engines, the cost of leasing and sending can be understood as: the spare engine prepared according to the forecast results is not enough to meet the actual spare engine response, and the actual spare engine needs to be met in the form of renting spare engine, and the corresponding leasing engine is generated. cost.

To sum up, in the proposed evaluation method for intermittent standby demand forecasting, the forecast deviation from the total cost index is as follows:

Among them, C _i represents the forecast cost deviation index of sample i;

Among them, y _i,pred and y _i,real represent the predicted value and actual value of the demand interval, respectively; d _{i, pred} and d _{i, real} represent the predicted value and actual value of the demand, respectively; c _rent and c _own represent the cost of rent and delivery, respectively rate and inventory cost rate; _c'rent and _c'own represent the deviation rate of rental and inventory and the deviation rate of inventory respectively; n represents the total number of forecast samples, and i represents the serial number of the forecast samples.

Other steps and parameters are the same as one of the first to fourth embodiments.

Adopt the following examples to verify the beneficial effects of the present invention:

Example 1:

Fleet spare demand forecasting comparative experiment:

In order to verify the Croston-XGBoost aero-engine spare demand forecasting model. The operation and maintenance data of the sample fleet from 2007 to 2016 are collected and obtained, and the daily observation sequence of standby demand is used as the original observation sequence of standby demand. It is a typical intermittent demand.

According to the framework of Croston's method, the original observation sequence of standby demand is decomposed into standby demand sequence and demand interval sequence. Through the decomposition of the original observation sequence of the standby demand of the sample fleet, a total of 213 pairs of standby demand and demand interval data were obtained. That is, the standby demand sequence is composed of 213 standby demand data arranged according to the demand response time sequence, and the standby demand interval sequence is composed of the corresponding 213 standby demand interval data. In the forecasting experiment of standby demand, the decomposed demand sequence and demand interval sequence are used as sample data.

In order to make full use of the limited spare demand samples, this paper adopts the sequential forecasting method to carry out the spare demand forecasting experiment. Sequential test: The demand samples for preparation and delivery are arranged according to the demand response time series. When the first m samples are used for the demand prediction experiment, the first (m-1) samples are used as training samples, and the mth sample is used as the test sample. In the spare engine demand prediction experiment, the minimum number of training samples was set to 5, and the 213 pairs of spare engine demand samples in the sample fleet were converted into 208 sets of training and test sets. In this paper's comparative experiments on demand forecasting, all machine learning methods use sequential testing.

As the fleet state is taken into account in the proposed Croston-XGBoost spare demand forecasting model. The demand forecasting experiment collects the fleet status information of the sample fleet when the standby demand response occurs, and uses the fleet status information as the covariate of the standby demand forecast and the standby demand interval forecast. Fleet status information utilized includes: total number of engines on the wing; total engine flight cycles on the wing; average engine flight cycles on the wing; total number of engines under repair; total engine flight cycles under repair; average engine flight cycles under repair; total number of engines available ; Total engine flight cycles available; Average engine flight cycles available.

In the XGBoost prediction model, RMSE is used as the training error evaluation parameter, the maximum decision tree depth is set to 8 layers, the learning rate is set to 0.1, and the maximum number of estimators is set to 800. Table 1 shows an example of the predicted spare demand and spare demand interval.

Table 1 Example of the forecast results of standby demand and demand interval

In order to compare the prediction accuracy of the Croston-XGBoost standby demand forecasting model, the traditional Croston method was used as the benchmark for the comparison experiment of standby demand forecasting. Support Vector Machine (SVM) and GBDT are used as comparative experimental methods. Table 2 and Table 3 show the forecast errors of spare capacity and demand interval of five groups of comparative experiments including the Croston-XGBoost spare demand forecasting model.

Table 2 Prediction error of standby demand

Table 3 Prediction error of standby demand interval

It can be seen from the above two tables that the XGBoost method obtains the best prediction accuracy in the prediction of spare demand interval. At the same time, due to the limited number of prepared samples, in the prediction experiment, the average of 10 prediction results of the BPNN method is taken as the final prediction result. In the forecasting of spare demand, the prediction accuracy of SVM method and BPNN method is better than that of XGBoost method, but the BPNN method still has a large prediction fluctuation.

In order to more comprehensively evaluate the demand forecast of intermittent standby power supply, in the comparative experiment of standby power supply demand forecast, the intermittent standby power supply demand forecast evaluation method proposed in this paper is used to comprehensively evaluate each group of standby power supply forecast models. The comprehensive evaluation takes the predicted total cost index as the evaluation index. The relevant cost ratios are set as: c _rent = 50; c _own = 20; c' _rent = 100 and c' _own = 150. The total cost index of forecast deviation for each forecast model is shown in Table 4.

Table 4 Comparison of the total cost of experimental prediction and evaluation

It can be clearly seen from the above table that the proposed Croston-XGBoost standby demand forecasting model obtains the minimum forecast deviation total cost index. Compared with the other four comparative experimental methods, the Croston-XGBoost spare engine demand prediction model has better comprehensive prediction performance and can provide basic support for the actual operation and maintenance of aero-engine fleets.

The present invention can also have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention, but these corresponding changes and deformations are all It should belong to the protection scope of the appended claims of the present invention.

Claims (2)

1. the Croston-XGBoost forecasting method of aero-engine standby demand is characterized in that: the method concrete process is: Step 1: Convert the original observation sequence of intermittent standby demand into standby demand interval sequence and standby demand sequence based on the Croston method; the specific process is as follows: Convert the original observation sequence of intermittent standby demand into standby demand interval sequence and standby demand sequence; The original observation sequence of intermittent standby demand is expressed as: Z={d ₀ ,0,...,0,d ₁ ,0,...,0,d _i ,0,...,0,d _n } (1) Among them, d _i represents the demand quantity of the i-th demand response, and d _i is a positive integer; The standby demand interval is defined as the observation interval of two adjacent demand responses; There are x _i+1 “0” value demands between two adjacent demand responses d _i and d _i+1 , then the demand interval sequence between d _i and d _i+1 is calculated by formula (2): y _i+1 = x _i+1 +1 (2) The original observation sequence of intermittent standby demand in the form of formula (1) is decomposed into a demand interval sequence and a demand quantity sequence, which are expressed as formula (3) and formula (4) respectively: Y=δ(Z)={y ₁ ,...,y _i ,...,y _n } (3) D=γ(Z)={d ₀ ,d ₁ ,...,d _i ,...,d _n } (4) Among them, D is the demand sequence, Y is the demand interval sequence; δ(*) and γ(*) are the conversion function functions of the demand interval sequence and the demand sequence, respectively, Z is the original observation sequence of intermittent standby demand, y ₁ is the first demand interval, y _i is the i-th demand interval, _yn is the n-th demand interval, d ₀ is the initial demand, d ₁ is the first demand, d _i is the i-th demand, d _n is the nth demand; Step 2: Build the XGBoost model; the specific process is: The XGBoost model is expressed as:

Among them, F represents the function space composed of all trees, {f ₁ ,f ₂ ,...,f _K } represents the K regression trees to be obtained by the XGBoost model,

represents the predicted value of sample i; x _i represents y _i or d _i ; The loss function of the XGBoost model is written as:

in,

prediction error for sample i, y _i and

are the actual value and predicted value of sample i, respectively; Ω(f _t ) is the regular term of the t-th regression tree, which is expressed as:

Among them, T represents the number of leaf nodes of the t-th regression tree, ω represents the weight of all leaf nodes of the t-th regression tree, γ is the coefficient of the leaf node, and λ is the L ₂ regular penalty coefficient; the predicted value of sample i is expressed as The form of formula (8), the loss function is expressed as the form of formula (9):

in,

is the predicted value of sample i in t trees,

is the predicted value of sample i in the existing t-1 tree, f _t is the regression tree with the smallest loss function based on the existing t-1 tree, f _t ( _xi ) is the sample The value of i in the t-th optimal regression tree, Ω(f _t ) is the complexity of the t-th optimal regression tree; Taylor expansion of the loss function L ^(t) , the loss function is expressed in the form of equation (10):

Among them, _gi and _hi are intermediate variables; _gi and _hi are specifically expressed as formula (11) and formula (12); The loss function with the constant term removed is expressed in the form of Equation (13):

in,

is the first derivative of the current error function,

is the second derivative of the current error function; Define I _j ={i|q( _xi )=j} as the jth leaf node, then

Expressed as formula (14):

Among them, q(x _i ) is the leaf node calculation function, which calculates the leaf node to which the sample i belongs; ω _j represents the weight of the jth leaf node of the tth regression tree; In order to find the minimum value of the loss function, the two ends of equation (14) are derived to obtain the optimal solution of ω _j

As shown in formula (15); using

Calculate the loss function to get equation (16):

Step 3. Based on Step 1 and Step 2, establish a demand interval forecasting model and a demand forecasting model for standby delivery; the specific process is as follows: Prediction model of spare demand interval O _y ={O _y1 ,O _y2 ,...,O _yn }; The forecasting model of the demand for spare hair O _d = {O _d1 ,O _d2 ,...,O _dn }; Step 4: Predict the deviation from the total cost index based on the interval forecasting model of the standby demand and the forecasting model of the standby demand obtained in the third step. 2. the Croston-XGBoost forecasting method of aero-engine standby demand according to claim 1, is characterized in that: in the described step 4, the standby demand interval prediction model and the standby demand prediction model obtained based on step 3, predict Deviation from the total cost index; the specific process is: Forecast deviation from the total cost index:

Among them, C _i represents the forecast cost deviation index of sample i;

Among them, y _i,pred and y _i,real represent the predicted value and actual value of the demand interval, respectively; d _{i, pred} and d _{i, real} represent the predicted value and actual value of the demand, respectively; c _rent and c _own represent the cost of rent and delivery, respectively rate and inventory cost rate; _c'rent and _c'own represent the deviation rate of rental and inventory and the deviation rate of inventory respectively; n represents the total number of forecast samples, and i represents the serial number of the forecast samples.

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