CN107886126A - Aerial engine air passage parameter prediction method and system based on dynamic integrity algorithm - Google Patents

Aerial engine air passage parameter prediction method and system based on dynamic integrity algorithm Download PDF

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CN107886126A
CN107886126A CN201711102389.0A CN201711102389A CN107886126A CN 107886126 A CN107886126 A CN 107886126A CN 201711102389 A CN201711102389 A CN 201711102389A CN 107886126 A CN107886126 A CN 107886126A
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CN107886126B (en
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钟诗胜
林琳
付旭云
张震
张一震
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Harbin Institute of Technology Weihai
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Abstract

The present invention relates to a kind of aerial engine air passage parameter prediction method and system based on dynamic integrity algorithm, wherein method includes：Training sample set is learnt based on iterative algorithm to obtain base learning machine, and test sample collection is predicted using base learning machine, obtains the prediction result of each base learning machine；Neighbour's sample of selection test sample is concentrated in the training sample, assesses the weights that each base learning machine is dynamically determined each base learning machine in the Local Property of neighbour's sample；Based on the weights of each base learning machine, the prediction result of each base learning machine is integrated into final prediction result using Density Estimator is weighted.The Local Property that the present invention passes through each learning machine of quantitative evaluation, propose dynamic weighting Density Estimator combined method, available in the prediction task to aerial engine air passage argument sequence, do not influenceed by outlier and sample are asymmetrically distributed, test result indicates that the precision of prediction of Ensemble Learning Algorithms can be effectively improved.

Description

Aero-engine gas path parameter prediction method and system based on dynamic integration algorithm
Technical Field
The invention relates to the technical field of prediction of aero-engine gas path parameters, in particular to a method and a system for predicting aero-engine gas path parameters based on a dynamic integration algorithm.
Background
The prediction of the performance parameters of the aero-engine is the basis of implementing the visual maintenance of the aero-engine, and the prediction of the performance parameters of the existing aero-engine mainly comprises support vector machine prediction, discrete process neural network prediction, a probability prediction method of a Combined Optimization Related Vector Machine (CORVM), fusion prediction, integrated learning algorithm prediction and the like. The gas path parameter prediction based on the single learning model belongs to a global modeling method, which can lead to the complexity of the model and is easy to fall into the local optimum. An ensemble learning algorithm that integrates multiple learning machines tends to achieve higher prediction accuracy than a single learning machine. Many scholars theoretically explore the effectiveness of ensemble learning. In recent years, ensemble learning has been increasingly applied to the problems of time series prediction and prediction of aircraft engine performance parameters. Integrated learning machines tend to achieve higher accuracy than single learning machines.
The combination methods adopted by the existing ensemble learning algorithm mostly belong to average (Mean), median (media) or their weighted forms. The combination method of the average and the weighted form thereof is easily affected by Outliers (Outliers), the asymmetry of the distribution (distributed asymmetry) has an effect on taking the average and the median and the weighted form thereof, and the combination method of Kernel Density Estimation (KDE) is not sensitive to the above two cases, but the local performance of the base learning machine is not taken into consideration in the prior art.
Disclosure of Invention
The technical problem to be solved by the invention is that aiming at the problem that a combination method based on averaging and median taking is easily influenced by outliers and asymmetric distribution, local performance evaluation and weighted kernel density estimation of a base learning machine are combined, a Dynamic Weighted Kernel Density Estimation (DWKDE) combination method is provided, and the aero-engine gas path parameters are predicted to obtain an aero-engine gas path parameter prediction method and a system combination method based on a dynamic integration algorithm.
In order to solve the technical problem, in a first aspect of the present invention, a method for predicting an aero-engine gas path parameter based on a dynamic integration algorithm is provided, which includes the following steps:
an iterative training step, learning a training sample set based on an iterative algorithm to obtain a base learning machine, and predicting a test sample set by using the base learning machine to obtain a prediction result of each base learning machine;
a weight determination step, namely selecting a neighbor sample of a test sample in the training sample set, and evaluating the local performance of each base learning machine in the neighbor sample to dynamically determine the weight of each base learning machine;
and integrating prediction, namely integrating the prediction result of each base learning machine by utilizing weighted kernel density estimation based on the weight of each base learning machine to obtain a final prediction result.
In the method for predicting the gas circuit parameters of the aircraft engine based on the dynamic integration algorithm, preferably, the step of determining the weight value comprises the following steps:
(1) For a test sample Q, calculating the distances between all training samples and the test sample Q, arranging the training samples in the order from small to large, and selecting K adjacent samples according to a K adjacent method;
(2) Calculating Euclidean distances from the K neighbor samples to the test sample Q, and normalizing to obtain a normalized distance; calculating a weighted average absolute value error;
(3) And for the test sample Q, calculating a weight corresponding to the t-th base learning machine based on the weighted average absolute value error.
In the method for predicting the gas circuit parameters of the aircraft engine based on the dynamic integration algorithm, the iterative training step preferably includes the following iterative steps for the tth base learning machine:
(1) In the case that the sample weight distribution is D t Training sample setTraining a tth base learning machine;
(2) Calculating the absolute value error predicted by the tth learning machine on the training sample to form a tth column of an absolute value error matrix E;
(3) Calculating the t-th base learning machine f t An error rate of (a);
(4) Update the sample weight D t 。
In the method for predicting the gas circuit parameters of the aircraft engine based on the dynamic integration algorithm, preferably, the iterative training step adopts an iterative algorithm of adaboost.rt or adaboost.r2 to learn the training sample set to obtain the base learning machine.
In a second aspect of the present invention, a system for predicting a gas path parameter of an aircraft engine based on a dynamic integration algorithm is provided, including:
the iterative training module is used for learning the training sample set based on an iterative algorithm to obtain a base learning machine, and predicting the test sample set by using the base learning machine to obtain a prediction result of each base learning machine;
the weight determination module is used for selecting a neighbor sample of the test sample in the training sample set, evaluating the local performance of each base learning machine in the neighbor sample and dynamically determining the weight of each base learning machine;
and the integrated prediction module is used for integrating the prediction result of each base learning machine by utilizing weighted kernel density estimation based on the weight of each base learning machine to obtain a final prediction result.
In the system for predicting the gas path parameters of the aircraft engine based on the dynamic integration algorithm according to the present invention, preferably, the weight determination module includes:
the neighbor sample selection unit is used for calculating the distances between all training samples and the test sample Q for the test sample Q, arranging the training samples in the order from small to large, and selecting K neighbor samples according to a K neighbor method;
the absolute value error calculation unit is used for calculating Euclidean distances from the K neighbor samples to the test sample Q and obtaining a normalized distance after normalization processing; calculating a weighted average absolute value error;
and the weight calculation unit is used for calculating the weight corresponding to the t-th base learning machine based on the weighted average absolute value error for the test sample Q.
In the system for predicting the gas circuit parameters of the aircraft engine based on the dynamic integration algorithm, preferably, the iterative training module executes the following iterative steps for the tth base learning machine:
(1) In the sample weight distribution of D t Training sample setTraining a tth base learning machine;
(2) Calculating the absolute value error predicted by the tth learning machine on the training sample to form a tth column of an absolute value error matrix E;
(3) Calculating the t-th base learning machine f t The error rate of (a);
(4) Update the sample weight D t 。
In the aircraft engine gas circuit parameter prediction system based on the dynamic integration algorithm, the iterative training module learns the training sample set by adopting an iterative algorithm of AdaBoost.RT or Adaboost.R2 to obtain the base learning machine.
The method and the system for predicting the gas circuit parameters of the aero-engine based on the dynamic integration algorithm have the following beneficial effects: the invention provides a dynamic weighted kernel density estimation combination method by quantitatively evaluating the local performance of each learning machine, the combination method is adopted for integrated learning, the combination method can be used for predicting a gas circuit parameter sequence of an aircraft engine, and the aircraft engine gas circuit parameter prediction method based on the dynamic integrated algorithm is obtained.
Drawings
Fig. 1 is a flowchart of a method for predicting a gas path parameter of an aircraft engine based on a dynamic integration algorithm according to a first embodiment of the invention;
fig. 2 is a flowchart of a conventional adaboost.
FIG. 3 is a schematic frame diagram of a method for predicting a gas path parameter of an aircraft engine based on a dynamic integration algorithm according to the present invention;
FIG. 4 is a flowchart of a method for predicting a gas path parameter of an aircraft engine based on a dynamic integration algorithm according to a second embodiment of the invention;
FIG. 5 is a block diagram of a system for predicting gas path parameters of an aircraft engine based on a dynamic integration algorithm according to a preferred embodiment of the present invention;
FIG. 6 is a schematic diagram of a weight determination module in a dynamic integration algorithm based aero-engine gas path parameter prediction system according to a preferred embodiment of the present invention;
FIG. 7 is a graph of the distribution of the Mackey-Glass time series used in the validation of the present invention;
FIG. 8 is a graph of the results of calculations for each ensemble learning machine;
FIGS. 9a to 9d are graphs showing the variation tendency of MAE, RMSE, MAPE and MASE with the number of the learning machines;
FIG. 10a is the predicted result of DWRT versus Mackey-Glass test set, and FIG. 10b is an enlarged view of the maximum absolute value error.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
Referring to fig. 1, a flowchart of a method for predicting a gas path parameter of an aircraft engine based on a dynamic integration algorithm according to a first embodiment of the present invention is shown. As shown in fig. 1, the method for predicting the gas path parameters of the aircraft engine based on the dynamic integration algorithm provided by the embodiment includes the following steps:
first, in step S101, an iterative training step is performed, a training sample set is learned based on an iterative algorithm to obtain a base learning machine, and a test sample set x is subjected to learning by using the base learning machine new And predicting to obtain the prediction result of each base learning machine. For example, training sample set x is subjected to iterative algorithm new Base learning machine for learningAnd obtain each base learning machinePredicted result of (2)The iterative algorithm is preferably adaboost.rt and adaboost.r2.
Subsequently, in step S102, a weight determination step is performed, a neighboring sample of the test sample is selected in the training sample set, and the local performance of each base learning machine in the neighboring sample is evaluated to dynamically determine the weight of each base learning machine. Preferably, the weight determining step specifically includes:
(1) For test sample set x new For the test sample Q in (1), calculating the distances between all training samples and the test sample Q, arranging the training samples in the order from small to large, and selecting K adjacent samples according to a K adjacent method;
(2) Calculating Euclidean distance d from K adjacent samples to test sample Q i I =1 \ 8230k, and obtaining the normalized distance d after normalization treatment i '; and calculating a weighted average absolute value error:
wherein e ti The prediction error of the ith neighbor sample of the test sample Q for the tth base learning machine is T =1, \ 8230; and e ti ＝f ti -y i ，f ti Predicted value, y, for the ith base learning machine for the ith neighbor sample i The true output value of the ith neighbor sample.
(3) For the test sample Q, calculating a weight corresponding to the t-th base learning machine based on the weighted average absolute value error:
wherein Z is a normalization factor, such that
Finally, in step S103, an integration prediction step is performed to integrate the prediction results of each base learning machine by using weighted kernel density estimation based on the weight of each base learning machine to obtain a final prediction result. Preferably, each base learning machine is integrated in the prediction step by the following formulaPredicted result of (2)And integrating to obtain a final prediction result:
wherein s is t As a result of prediction of the t-th base learning machine, w tQ Is the weight corresponding to the t-th base learning machine, and K (-) is the kernel functionAnd h is the bandwidth.
The invention provides a Dynamic Weighted Kernel Density Estimation (DWKDE) combination method by quantitatively evaluating the local performance of each learning machine, and the combination method is used for integrated learning and can be used for predicting a task of an aeroengine gas path parameter sequence to obtain the aeroengine gas path parameter prediction method based on the Dynamic integrated algorithm, and the combination method is not influenced by outliers and asymmetric sample distribution.
The method can be applied to AdaBoost.RT and AdaBoost.R2 to respectively obtain DWRT (DWKDE-Based AdaBoost.RT) and DWR2 (DWKDE-Based AdaBoost.R2) integrated learning methods. That is, the iterative algorithm in step S101 may adopt adaboost.rt or adaboost.r2.
The principle and steps of the method for predicting the gas path parameters of the aircraft engine based on the dynamic integration algorithm are described in detail below.
1. Phase space reconstruction
The training sample and the testing sample of the aeroengine gas circuit parameters used in the invention are time sequences obtained by phase space reconstruction in advance.
Phase Space Reconstruction Theory (PSRT) is the basis of time series analysis. When predicting a time sequence, the sequence needs to be reconstructed to find the internal regularity of the sequence. The establishment and the use of the prediction model are completed in a phase space.
For time series, assume z m+h (h∈Z + ) The previous p (p ∈ Z) can be employed + ) A history data z m-p+1 ,…,z m-1 ,z m Predicted, as in formula (1):
z m+h ＝F(z m-p+1 ,…,z m-1 ,z m ) (1)
predicting the time series is equivalent to obtaining the formula (1) by adopting a learning algorithm. When h =1, it is referred to as one-step prediction of the time series, i.e., short-term prediction. While long-term prediction (h > 1) can be regarded as being iterated by multiple one-step predictionsIn the invention, one-step prediction is adopted.
Selecting the appropriate embedding dimension p, for the time seriesPerforming a phase space reconstruction to generate input and output samples for the one-step prediction, reconstructing the sequence, as shown in equations (2) and (3)
Time seriesThe sequence after reconstruction isIt can be used as a training sample set and a testing sample set for subsequent learning machines. The input and output of the training sample set are respectively marked as X train ,Y train The input and output of the test sample set are respectively marked as X test ,Y test . And the reconstructed sample can be used for training and verifying the model.
2. RT algorithm analysis and existing problems of the existing AdaBoost
The adaboost. Rt algorithm is an algorithm that applies adaboost. M1 to a regression problem. A threshold value of the absolute value of the relative error is introduced, and the training samples are divided into two types of correct prediction and wrong prediction. Experiments have shown that adaboost.rt is generally more predictive than another commonly used adaboost.r2, especially when the data contains outliers.
Please refer to fig. 2, which is a flowchart of the prior adaboost. As shown in fig. 2, the existing adaboost.
S201, starting a process;
s202, an input step, which comprises the steps of inputting the following data and parameters:
the set for training isy∈R；
Base learning algorithm Base Learner:namely, selecting a base learning machine;
specifying a total number of iterations T (also representing the number of generated base learning machines);
a threshold φ for the Absolute Relative Error (ARE) is specified.
S203, an initialization step:
let initial iteration number t =1;
setting M training samples to make the weights of the training samples distributed
Let error rate ε t ＝0。
In S204 to S209, an iterative process is performed, including:
s204, judging whether T = T, if so, turning to the step S205, otherwise, turning to the step S210;
s205, with sample weight D t Training sample setUpper training Base Learner;
s206, recording the t learning machine f t For the jth training sample x j Is predicted as f t (x j ) And the true output value is y j Calculating the prediction of the training sample for the tth learning machineAbsolute value error | f t (x j )-y i |；
S207, calculating the t base learning machine f t Error rate of (2):
is provided withn can be 1,2 or 3, and the invention preferably selects 1;
s208, updating the sample weight D t ：
Wherein Z t Is a normalization factor, guarantee D t+1 (j) Is a distribution, i.e.
S209, execute t = t +1, and go to step S204.
S210, executing an output step:
for test sample x new Each base learning machineThe prediction results are integrated to obtain a final prediction result:
rt algorithm, as can be seen from the above-mentioned existing adaboost, for any one test sample x new Predicted result of (f) t (x new ) In other words, the weight of the output result of the tth base learning machine is alwaysIt does not change with the change of the test sample. The integrated algorithm which is determined according to the weight of the base learning machine after training is called as the integrated learning algorithm based on static weight.
In each iteration process of the algorithm, sampling with replacement is carried out M times (making M = M) according to the sample weight value during each iteration, the training sample extracted each time does not contain all M samples, the training sample of each base learning machine is a subset of the original sample set, and the subsets used for training the learning machines are different. Therefore, the base learning machine obtained by the adaboost. The input of the training sample has multiple dimensions and can be grown into a high-dimensional space (for the test sample x) new And one point is represented in a high-dimensional space and is marked as Q), the training samples of all the learning machines are distributed in different spaces, and therefore the learning capabilities of all the base learning machines in different local spaces are inconsistent. Each learning machine in different local spaces should have different weights to ensure that the weight of the base learning machine with better predictive performance in the local space is larger, otherwise, the weight of the base learning machine is smaller. Local performance factors of the base learning machine should be taken into account to better predict new samples. Therefore, the weight of each learning machine is not fixed any more, but changes with the local space where the prediction sample is located, and the integration algorithm is called as a dynamic integration algorithm, and can generally obtain better effect than a static integration algorithm.
Rt is a weighted average approach. The combination method of the average and the weighted form thereof is susceptible to the influence of outliers, the asymmetry of the distribution has an influence on the combination method of taking the average and taking the median and the weighted form thereof, and the KDE combination method is insensitive to both of the above two cases.
3. The invention discloses a dynamic weighted kernel density estimation ensemble learning method
In view of the problems of adaboost.rt, the present invention introduces the local performance evaluation of the learning machine into the kernel density estimation to obtain the weighted kernel density estimation, and the weight thereof can be dynamically changed according to different test samples. The following describes a dynamic weighted kernel density estimation combination method of the present invention that combines weighted kernel density estimation with local performance evaluation of a base learning machine.
3.1 weighted Kernel Density estimation
Kernel density estimation is a method of estimating a density function expression from sample data. Learning machine with T basesSample x to be predicted new The set of predicted results (point Q) isIts kernel density function is p(s). Then p: ( s ) Is expressed in the form of:
in the formula, T is the number of the base learning machines, and T is generally required to be more than or equal to 30 in order to ensure the nuclear density estimation effect; k (-) is a kernel function; h is the bandwidth; w(s) t ) Is a weight value.
As can be seen by definition, the kernel function is a weight function that utilizes the data point s in estimating the kernel density of the point s t Distance to s (s-s) t ) And s t Corresponding w(s) t ) To determine s t The magnitude of the importance of. The factors determining the weighted kernel density estimation expression include kernel function, window width and w(s) t ).
In general, the choice of kernel function is not the most critical factor in kernel density estimation, butThe smoothness of (d) is mainly determined by the window width h, which directly determines the estimation effect. Commonly used one-dimensional kernel functions include gaussian kernel functions, uniform kernel functions, exponential kernel functions, and the like. The present invention preferably employs a commonly used gaussian kernel function, which is defined as equation (5).
Selection of bandwidth h versus estimationIt is crucial that if h is too large, thenIt will appear too smooth, ignoring some details; if h is too small, thenThe curve (especially the tail) may fluctuate greatly. The main selection method comprises the following steps: thumb method, maximum likelihood estimation method, optimal theoretical window width and least square cross-validation method. The bandwidth calculated using the thumb method is sufficient for the gaussian kernel. The bandwidth calculation formula is as shown in equation (6).
In the formula (I), the compound is shown in the specification,is thatStandard deviation of (2).
Enabling kernel density function estimationThe s at which the maximum point is obtained is denoted as s Mode I.e. the value after the integration of each learning machine, the calculation formula is as shown in equation (7). Meanwhile, since the kernel density estimation requires a large number of prediction values (i.e., a large number of base learning machines), generally, an ideal result can be obtained when the number of the base learning machines is greater than 30.
Then theIs to determine w(s) t ) I.e. the local performance of the base learning machine needs to be evaluated.
3.2 local Performance evaluation of learning machines
The prediction capability of the learning machine on the test sample Q is related to the learning capability of the learning machine on the adjacent sample, so that the prediction quality of the learning machine on the test sample Q can be evaluated through the prediction quality of the adjacent sample, and the weight corresponding to the base learning machine is further determined through the prediction effect on the adjacent sample.
Therefore, the weight determination step of the method for predicting the gas path parameters of the aircraft engine based on the dynamic integration algorithm, namely the step S102, comprises the following 3 steps: (1) finding x in training sample set according to certain criterion new (Q) neighbor samples; (2) evaluating the prediction performance of each learning machine on a neighboring sample; (3) and determining the weight value of the base learning machine.
1) Finding x in a training sample set new Of (2) neighbor samples
Finding a test sample x in a training sample set new The process of the neighbor samples is the process of measuring the similarity between different sequences. The Time series distance measurement method mainly includes a Minkowski (Minkowski) distance, a Longest Common Substring (LCS) distance, a cosine similarity, a Dynamic Time Warping (DTW) distance, and the like. The most commonly used is the Minkowski distance, assuming an input vector of two samples of<v 1 ,v 2 ,…,v p &gt, and<v′ 1 ,v′ 2 ,…,v′ p &then the Minkowski distance can be expressed as formula (8):
when n =1, equation (8) becomes the manhattan distance; when n =2, it is the euclidean distance; when p = ∞ is called Chebyshev distance, i.e.Preferably, euclidean distances are used in the present invention to measure the distance between sequences.
Please refer to fig. 3, which is a schematic frame diagram of a method for predicting an aircraft engine gas path parameter based on a dynamic integration algorithm according to the present invention. As shown in fig. 3, a dashed box a illustrates selection of neighboring samples (only 5 neighboring samples are taken as an example in the figure, and the present invention is not limited thereto), a dashed box B illustrates evaluation of local performance of each base learning machine in the neighboring samples to dynamically determine a weight of each base learning machine, and a dashed box C illustrates a process of performing integrated prediction by using weighted kernel density estimation. Therefore, it can be seen from section a that the step of selecting the neighbor samples of the test sample in the training sample set specifically includes: for the test samples Q in the test sample set, the distances between all the training samples and the test samples Q are calculated and arranged from small to large, and K adjacent samples are selected according to a K-Nearest Neighbor method (K-NN).
2) Evaluating local performance of each learning machine on its neighbor samples
Calculating the Euclidean distance d from the K neighbor samples to the test sample Q i ,i＝1…K；
After normalization processing, normalized distance is obtained:
let the real output of i neighbor samples be y i I =1, \8230, K, and the predicted value of the t-th base learning machine to the i-th adjacent sample is set as f ti ,t＝1,…,T。
The Weighted Mean Absolute Error (WMAE) is calculated and is defined in the present invention as equation (10):
wherein e ti The prediction error of the ith adjacent sample of the test sample Q for the tth base learning machine is T =1, \8230, and T are the number of the base learning machines; and e ti ＝f ti -y i ，f ti Predicted value, y, for the t-th base learning machine for the i-th neighbor sample i The true output value of the ith neighbor sample.
It can be seen that WMAE takes into account both the absolute value error of the learning machine on the neighboring samples of Q and the distance of the neighboring samples to Q. The closer the sample is to Q, the greater its impact on the learning machine performance assessment. In the neighborhood of Q, corresponding to the base learning machine with good prediction performanceIs small; conversely, it is larger. The weight of the base learning machine can be determined from WMAE.
3) Determining a weight
For the test sample Q, calculating a weight corresponding to the tth base learning machine based on WMAE, as shown in formula (11):
wherein Z is a normalization factor, such that
Calculated w tQ I.e., the weight w(s) of the t-th base learning machine in section 3.1 t )。
3.3 dynamic weighting kernel density estimation combination method and ensemble learning method
The invention combines the kernel density estimation combination method and the local performance evaluation of the learning machine to obtain the Dynamic Weighted Kernel Density Estimation (DWKDE) combination method. The combination method can dynamically adjust the weight, and the contribution weight of the base learning machine with high prediction precision in the local space where Q is located is larger; otherwise, the contribution weight is smaller, and the weight is the weight required by the weighted kernel density estimation.
The DWKDE combination method is applied to the AdaBoost. Therefore, the invention provides a second embodiment of the method for predicting the gas path parameters of the aircraft engine based on the dynamic integration algorithm. Referring to fig. 4, a flowchart of a method for predicting a gas path parameter of an aircraft engine based on a dynamic integration algorithm according to a second embodiment of the present invention is shown. The process comprises the following steps:
s401, starting a process;
s402, an input step, which comprises the steps of inputting the following data and parameters:
the set for training isy∈R；
Base learning algorithm Base Learner:namely, selecting a base learning machine;
specifying a total number of iterations T (also representing the number of final generation base learning machines);
a threshold value φ of an Absolute Relative Error (ARE) is specified. The training samples are divided into samples that are predicted correct and samples that are predicted incorrect according to phi.
S403, initialization step:
let initial iteration number t =1;
m training samples are arranged, so that the weight distribution of the training samples is realized during the first training
Let the error rate epsilon t ＝0；
Let the absolute value error matrix E be an mxt zero matrix, where each column of the matrix stores a value representing the absolute value error predicted by each learning machine for each training sample.
In S404 to S409, an iterative process is performed, including:
s404, judging whether T = T, if yes, turning to the step S405, and if not, turning to the step S410;
s405, distributing weight as D t Training sample setThe T-th Base Learner (Base learning machine) is trained, T =1, \8230, T, T is the number of the Base learning machines;
s406, calculating the absolute value error predicted by the tth learning machine on the training sample to form the tth column of an absolute value error matrix E: e (j, t) = | f t (x j )-y j |,j＝1,…M；f t (x j ) For the t-th base learning machine f t For the jth training sample x j Predicted result of (2), y j The true output value of the jth training sample is obtained;
s407, calculating the t-th base learning machine f t Error rate of (2):
wherein phi is a preset threshold value of the absolute value of the relative error;
is provided withn is 1,2 or 3; the invention preferably selects 1;
s408, updating the sample weight D t ：
Wherein Z t Is a normalization factor, guarantee D t+1 (j) Is a distribution, i.e.
S409, t = t +1 is executed, and step S410 is turned over.
S410, determining the weight of the base learning machine, including:
1) Selecting a neighbor sample
For a test sample Q, calculating the distances between all training samples and the test sample Q, arranging the training samples in the order from small to large, and selecting K adjacent samples according to a K adjacent method;
2) Local performance evaluation and weight determination of base learning machine
Finding the absolute value error of each base learning machine for K adjacent samples from the absolute value error matrix E, and calculating the weighted average absolute value error according to the formula (9) and the formula (10)
Calculating the weight w of the t-th base learning machine to the Q prediction result according to the formula (11) tQ 。
S411, executing an output step:
for test sample x new Each base learning machineThe predicted results of (a) are integrated to obtain the final predicted result:
each base learning machinePredicted result of (2)Integrated to get the final prediction:
the aircraft engine gas path parameter prediction method based on the dynamic integration algorithm in the third embodiment of the invention is to apply the DWKDE combination method to Adaboost. R2 ensemble learning method, and a DWR2 method can be obtained. The steps of the third embodiment are similar to those of the second embodiment, and are not repeated herein.
Preferably, step S405 of the present invention requires that the base learning machine can learn data with a specific distribution, and a "Weighting method" (Re-Weighting) can be used; for a base learning machine which cannot process samples with weights, a 'resampling method' (Re-Sampling) should be adopted, that is, resampling is carried out according to sample weights each time, samples obtained through resampling are trained, and then training sample weights are updated according to training results. The invention selects the base learning machine as the neural network, and the neural network can not process the samples with weights, so the 'resampling method' is selected.
In the sample weight updating step S408, the step t is performed by the base learning machine f t (x) The weight of the correctly predicted samples will be smaller, while the weight of the incorrectly predicted samples will be relatively larger. Then, when the step t +1 is re-sampled, the probability that the correct sample in the step t is re-sampled decreases, and the probability that the incorrect sample is re-sampled increases. It follows that the present invention will focus "attention" on "hard samples" that are predicted incorrectly. Here, "hard samples" refers to samples that are predicted to be less effective by a single learning machine.
Referring to fig. 5, a block diagram of a system for predicting a gas path parameter of an aircraft engine based on a dynamic integration algorithm according to a preferred embodiment of the present invention is shown. As shown in fig. 5, this embodiment provides a system 500 comprising: an iterative training module 501, a weight determination module 502 and an integrated prediction module 503.
The iterative training module 501 is configured to learn a training sample set based on an iterative algorithm to obtain a base learning machine, and predict a test sample set using the base learning machine to obtain a prediction result of each base learning machine. For example, training sample set x is subjected to iterative algorithm new Base learning machine for learningAnd obtain each base learning machinePredicted result of (2)The iterative algorithm is preferably adaboost.rt and adaboost.r2.
The weight determination module 502 is configured to select a neighboring sample of the test sample in the training sample set, and evaluate the local performance of each base learning machine in the neighboring sample to dynamically determine a weight of each base learning machine.
The integrated prediction module 503 is configured to integrate the prediction results of each base learning machine by using weighted kernel density estimation based on the weight of each base learning machine to obtain a final prediction result. Preferably, the ensemble prediction module 503 transforms each base learning machine by the following formulaPredicted result of (2)And (4) integrating to obtain a final prediction result:
wherein s is t As a result of prediction of the t-th base learning machine, w tQ Is the weight corresponding to the t-th base learning machine, K (-) is the kernel function, and h is the bandwidth.
Referring to fig. 6, a schematic diagram of a weight determination module in a system for predicting a gas path parameter of an aircraft engine based on a dynamic integration algorithm according to a preferred embodiment of the present invention is shown. As shown in fig. 6, preferably, the weight determination module 502 further includes: neighbor sample selection section 601, absolute value error calculation section 602, and weight calculation section 603.
The neighbor sample selection unit 601 is configured to calculate distances between all training samples and the test sample Q for the test sample Q, arrange the distances in an order from small to large, and select K neighbor samples according to a K neighbor method;
the absolute value error calculating unit 602 is used for calculating the euclidean distance d from the K neighbor samples to the test sample Q i I =1 \ 8230K, and obtaining a normalized distance d after normalization processing i '; and calculating a weighted average absolute value error:
wherein e ti The prediction error of the ith neighbor sample of the test sample Q for the tth base learning machine is T =1, \ 8230; and e ti ＝f ti -y i ，f ti Predicted value, y, for the ith base learning machine for the ith neighbor sample i The true output value of the ith neighbor sample;
the weight calculation unit 603 is configured to calculate, for the test sample Q, a weight corresponding to the tth base learning machine based on the weighted average absolute value error:
wherein Z is a normalization factor, such that
When the prediction system of the air path parameters of the aircraft engine based on the dynamic integration algorithm is realized by combining the AdaBoost. RT algorithm, the iterative training module 501 executes the following iterative steps for the t-th base learning machine:
(1) In the case that the sample weight distribution is D t Training sample setTraining a tth base learning machine, wherein T =1, \8230, and T is the number of the base learning machines;
(2) Calculating the absolute value error predicted by the t learning machine on the training sample to form the t column of an absolute value error matrix E: e (j, t) = | f t (x j )-y j |,j＝1,…M；f t (x j ) For the t-th base learning machine f t For the jth training sample x j Predicted result of (1), y j The true output value of the jth training sample is obtained;
(3) Calculating the t-th base learning machine f t Error rate of (2):
wherein phi is a preset threshold value of the absolute value of the relative error;
is provided withn is 1,2 or 3;
(4) Update the sample weight D t ：
Wherein Z t Is a normalization factor, such that
Specific application examples of the present invention will be described below.
1. Validity verification
The algorithm adopted by the invention comprises a neural network, an original AdaBoost.RT method and an AdaBoost.RT algorithm adopting a KDE combination method (weight w corresponding to the prediction result of each base learning machine in the formula (4) tQ All 1/T, no local performance evaluation step, and the rest calculation stepsConsistent with the DWRT algorithm of the present invention), an adaboost.rt algorithm using a DWKDE combination method (i.e., the second embodiment of the present invention), an original adaboost.r2 method, an adaboost.r2 algorithm using a KDE combination method, and an adaboost.r2 algorithm using a DWKDE combination method (i.e., the third embodiment of the present invention), which are respectively denoted as NN, ORT, KDERT, DWRT, OR2, KDER2, and DWR2 for convenience of description.
The validity of the proposed algorithm is verified by using the commonly used Mackey-Glass time series, which can be generated by equation (12). The following 4 indices were used to evaluate the predicted effect: mean Absolute Error (MAE), RMSE, mean Absolute Percent Error (MAPE), and Mean Absolute Scaled Error (MASE).
According to "LI C, HU J W.A new ARIMA-based neuro-fuzzy approach and sweep interaction for time series for evaluating [ J]Engineering Applications of Artificial Intelligence,2012,25 (2): 295-308. "(abbreviated as comparison document 1) sets α =0.2, β =0.1, τ =17, z (0) =1.2 and z (t) =0 when t < 0. The sequence was generated according to equation (12), and 1000 data points of t =118-1117 were selected and recorded asAs shown in fig. 7. The first 500 points are selected to predict the next 500 points. And selecting a neural network as a generation algorithm of a base learning machine, and predicting by adopting a one-step prediction method.
The structure of the neural network is chosen to be 8-30-1, then p =8 at the phase space reconstruction. The method specifically comprises the following steps: the training maximum iteration number is 200, the training precision is that Mean Squared Error (MSE) reaches 0.00001, the learning rate is 0.1, the training algorithm is selected to be Levenberg-Marquardt (LM) algorithm, the hidden layer activation function is a Log-Sigmoid function, and the output layer activation function is a linear function. The experimental setup is summarized in table 1.
TABLE 1 Mackey-Glass sequence Experimental setup
All experiments were repeated 10 times to take the average. The prediction results for the test set are shown in table 2, with the optimal values for each index shown in bold. The percentage improvement in prediction accuracy of DWRT over individual NN, ORT and KDERT is shown in table 3.
TABLE 2 Mackey-Glass sequence prediction effect (T = 40)
Table 3 DWRT prediction accuracy improvement percentage (T = 40)
As can be seen from tables 2 and 3, the prediction accuracy is effectively improved compared with that of each of NN, ORT and KDERT, but the improvement amplitude is not large, and the prediction accuracy of KDERT and ORT is basically consistent. The DWRT provided by the invention can greatly improve the prediction precision.
When predicting the first data point of the test set, the prediction results of the 40 base learning machines are drawn as a histogram, and the calculation results of the ensemble learning machines are also shown, as shown in fig. 8. The ordinate of the DWRT and KDERT kernel density estimation curves (marked by letters D and K in figure 8 respectively) is 'kernel density', and the ordinate of the statistical result of the prediction result of each base learning machine is 'frequency'. The difference of the kernel density estimation curves of the KDERT algorithm adopting the KDE combination method and the DWRT algorithm adopting the DWKDE combination method can be seen. DW (DW)The RT prediction results are closest to the true value, KDERT times, and the ORT prediction results (denoted by the letter O in FIG. 8) are farthest from the true value (denoted by the letter R in FIG. 8). When a KDERT algorithm estimates a kernel density curve, the weight w in the formula (4) tQ Are all 1/T, and when the DWRT algorithm estimates the kernel density curve, the weight w in equation (4) tQ The calculation formula of (c) is formula (11). As can be seen from FIG. 4, although the kernel density curve of KDERT is closer to the distribution of the true prediction result than the kernel density curve of DWRT, because the prediction precision of each learning machine in the local space of the sample is not consistent, a new w can be obtained tQ Further, the kernel density curve of KDERT is adjusted to the kernel density curve of DWRT. It can be seen that although the distribution of the prediction results cannot be well reflected by the nuclear density curve of the DWRT, the DWRT algorithm considers the local performance difference of the base learning machines and gives different weights to the prediction results of each base learning machine, so that the learning machine with a good prediction effect in the test sample local space has a larger weight, the obtained nuclear density estimation curve can effectively reflect the distribution of the prediction results considering the local performance of the learning machine, and the DWRT algorithm can obtain a better prediction result.
To study the effect of the number of base learning machines T on the ensemble learning machine, T was initially set to 5, then T was set to increase from 10 to 150, each increment was 10, the rest of the experiment settings were consistent with table 1, the experiment was repeated 10 times, and the average of 10 predictions was taken as the final prediction. The trend of the MAE, RMSE, MAPE and MASE with the number of the base learning machines T is shown in FIGS. 9a to 9d, respectively.
As can be seen from fig. 9a to 9d, in each evaluation index, each ensemble learning machine can effectively improve the prediction accuracy, which indicates that the ensemble learning machine can actually effectively improve the prediction accuracy with respect to a single learning machine, and as the number of the basis learning machines increases, each ensemble algorithm can effectively improve the prediction accuracy. However, when the number of the base learning machines is too large, the prediction accuracy improvement range becomes small and even oscillation occurs. When the number T of the base learning machines is increased from 5 to 40, the prediction accuracy of each ensemble learning machine can be greatly improved, the ORT, the KDERT and the DWRT are respectively reduced by 7.49%, 13.97% and 36.49% on the RMSE index, when the number T of the base learning machines is increased from 40 to 70, the prediction accuracy of each ensemble learning machine can be slightly improved, and the ORT, the KDERT and the DWRT are respectively reduced by 4.94%, 5.31% and 10.08% on the RMSE index. When T is increased from 70 to 150, ORT, KDERT and DWRT are only respectively reduced by 2.09%, 3.47% and 7.28% on the RMSE index, and it can be seen that the prediction precision improvement amplitude of the ensemble learning machine is very limited at the moment, and even small-amplitude oscillation can occur in the process.
And when the number T of the base learning machines is less than 40, the prediction accuracy of the KDERT algorithm adopting the KDE combination method is lower than that of the ORT algorithm. This is mainly due to the fact that KDERT uses KDE combining methods, and the kernel density estimation results unreliable when there are few data points. When T is more than 40 and less than 100, the prediction precision of KDERT is basically consistent with that of ORT, because when the number of data points is more, the kernel density estimation can obtain a more reliable result, and the KDE combination method can be an effective combination method. When T is greater than 100, according to the 4 indexes, the prediction accuracy of KDERT is slightly higher than ORT, because the reliability of the kernel density estimation can be further improved by continuously increasing data points, and a better prediction effect can be obtained.
As can be seen from fig. 9a to 9d, in general, regardless of the value of T, the DWRT algorithm using the dynamic weighted kernel density combination method proposed herein can achieve the best results compared to NN, ORT, and KDERT; compared with ORT and KDERT, the prediction accuracy of the DWRT algorithm can be greatly improved by increasing T. Furthermore, as can be seen from fig. 9b, in the RMSE index, ORT achieves a minimum value of 0.001687 at T =150, kdert achieves a minimum value of 0.001661 at T =140, and DWRT corresponds to an RMSE of 0.001434 at T = 5. Therefore, compared with the ORT algorithm when T =150 and the KDERT algorithm when T =140, DWRT can obtain better prediction results only by 5 base learning machines, and the complexity of the algorithm is greatly reduced.
The invention adopts the same time sequence as the comparison file 1 and has the same training set and test set division, and the RMSE of the NFS-ARIMA (4, 0) and NFS-ARIMA (4, 1, 0) models on the test set is 0.0013 and 0.00086 respectively. DWRT presented herein calculated RMSE at T =40,80,100 as 0.00091, 0.00088 and 0.00078, respectively. DWRT can take the minimum RMSE of 0.00076, when T =140.
In conclusion, the DWRT method adopting the DWKDE combination method provided by the invention is a better integrated learning machine. Compared with the ORT and KDERT algorithms, the DWRT method can obtain the best prediction effect. The invention proposes that when using the DWRT method, the number of learning machines can be between 40 and 70, where a higher prediction accuracy can be obtained while using fewer NNs.
When T =100, the DWRT prediction results are shown in fig. 10a and 10 b. Wherein, FIG. 10a is the predicted result of DWRT to Mackey-Glass test set, and FIG. 10b is the enlarged view of the place with the maximum absolute value error.
In addition, comparative experiments were performed using OR2, KDER2 and DWR2. R2 calculates the loss function in a Linear Form (Linear Form) as set forth herein. Let T =40, the rest experimental settings are consistent with those of adaboost. The prediction results for the test sample set are shown in table 6, where the optimal values for each index are shown in bold.
Table 6 Mackey-Glass sequence predicted effect (T =40, based on adaboost. R2)
As can be seen from table 6, RMSE of KDER2 algorithm decreased by 76.08% relative to OR2, which shows the effectiveness of the KDE combination method. Meanwhile, when the DWR2 algorithm based on the DWKDE combination method is adopted, the RMSE is reduced by 88.04 percent relative to OR2, 50.00 percent relative to KDER2 and 61.95 percent relative to single NN. It can be seen that the effect of OR2 is poor, even worse than that of a single NN, which is mainly because the sample weight update strategy of OR2 causes the method to be very sensitive to abnormal samples, which are trained sufficiently but not well. Comparing table 2 and table 6, it can be seen that, in the four evaluation indexes, the prediction accuracy of KDER2 is higher than KDERT, and the prediction accuracy of DWR2 is higher than DWRT, which indicates that the prediction accuracy is often inferior to adaboost. "override" of prediction accuracy can be achieved by means of a KDE and DWKDE combination method.
The combination method of OR2 belongs to the form of Weighted Median (Weighted media), the combination method is susceptible to the influence of asymmetric distribution of samples, the weight updating mode of the OR2 algorithm makes the OR2 algorithm sensitive to abnormal samples, the KDE combination method and the DWKDE combination method can make up for the defect of the OR2 algorithm, and DWR2 can obtain a better result than KDER 2.
Therefore, the DWKDE combination method is also suitable for AdaBoost.R2, and the prediction precision can be improved.
2. Prediction of gas path parameters of aircraft engine
The failure types of the aero-engine are complex, more than 90 percent of the engine failures are gas circuit component failures, and the cost for maintaining the gas circuit components accounts for 60 percent of the total maintenance cost of the engine [21] . Therefore, gas circuit component fault diagnosis plays an important role in EHM systems. Important gas path parameters of the engine are exhaust temperature (EGT), low-pressure rotor rotating speed (N1), core machine rotating speed (N2) and Fuel Flow (FF), wherein N1 is a thrust parameter of the engine, and prediction objects of the gas path parameters of the aeroengine are exhaust temperature margin (EGTM), core machine rotating speed deviation value (delta N2) and fuel flow deviation value (delta FF).
And selecting a 1300-cycle EGTM sequence, a delta N2 sequence and a delta FF sequence for experiment, selecting a neural network as a base learning machine generation algorithm, and predicting by adopting a one-step prediction method. The topological structures of the neural networks adopted for the 3 parameter sequences are 6-10-1, 8-15-1 and 6-15-1 respectively. The specific settings of the experiment employed were: the maximum iteration number of training is 200, the training precision is that mean square error respectively reaches 0.0001, 0.00001 and 0.00001, the learning rate is 0.05, the training algorithm is selected as Levenberg-Marquardt (LM) algorithm, the activation function of an output layer is set to be a linear function, and the activation function of a hidden layer is a Log-Sigmoid function. Other relevant configurations of the experiment are shown in table 7.
Table 7 gas path parameter sequence prediction experiment configuration
The 3 gas circuit parameters are tested by adopting a single neural network, ORT, KDERT, DWRT, OR2, KDER2 and DWR2 algorithm, each test is repeated for 10 times, and the average value is taken as the final prediction result. The results of the experiments on the test set are shown in tables 8 to 10, in which the optimum values for each index are shown in bold.
TABLE 8 EGTM sequences predicting Effect
TABLE 9 Δ N2 sequences prediction Effect
TABLE 10. DELTA.FF sequences predict effect
As can be seen from the experimental results in tables 8 to 10, the ensemble learning algorithms (DWRT and DWR 2) using the DWKDE combining method proposed herein can achieve the best results, while the prediction accuracy of the ensemble learning algorithm using the KDE combining method is consistent with that of the original ensemble learning algorithm or the accuracy improvement is not large.
Therefore, the DWRT (second embodiment) and the DWR2 algorithm (third embodiment) adopting the DWKDE combination method provided by the invention can be suitable for the prediction task of the gas path parameters of the aeroengine, and can effectively improve the prediction precision, compared with other algorithms, the root mean square error of the DWRT and the DWR2 can be reduced by at least 27%.
In summary, the invention provides a new combination method, namely a Dynamic Weighted Kernel Density Estimation (DWKDE) combination method, by combining local performance evaluation and weighted kernel density estimation of a base learning machine aiming at the problem that the combination method based on average and median taking is easily influenced by outliers and asymmetric distribution. Based on the combination method, DWRT and DWR2 ensemble learning algorithms are provided. The invention also defines the steps of calculating the local performance of the base learning machine from the neighbor samples of the test sample and combining with the weighted kernel density estimation to construct a DWKDE combination method. Experiments on the Mackey-Glass sequence show that the DWRT and DWR2 algorithms can effectively improve the prediction precision, can still obtain higher prediction precision under the condition of using less base learning machines, and reduces the calculation complexity. By means of this combined approach, adaboost.r2 can achieve "overrun" to adaboost.rt. Prediction experiment results of aero-engine gas path parameter sequences (EGTM, delta N2 and delta FF) show that the DWRT and DWR2 algorithms can be suitable for aero-engine gas path parameter prediction tasks, and prediction accuracy can be effectively improved.

Claims (10)

1. An aircraft engine gas path parameter prediction method based on a dynamic integration algorithm is characterized by comprising the following steps:
an iterative training step, learning a training sample set based on an iterative algorithm to obtain a base learning machine, and predicting a test sample set by using the base learning machine to obtain a prediction result of each base learning machine;
a weight determination step, namely selecting a neighbor sample of the test sample in the training sample set, and evaluating the local performance of each base learning machine in the neighbor sample to dynamically determine the weight of each base learning machine;
and integrating prediction, namely integrating the prediction results of each base learning machine by using weighted kernel density estimation based on the weight of each base learning machine to obtain a final prediction result.
2. The method for predicting the gas circuit parameters of the aero-engine based on the dynamic integration algorithm as claimed in claim 1, wherein the weight determining step comprises the steps of:
(1) For a test sample Q, calculating the distances between all training samples and the test sample Q, arranging the training samples in the order from small to large, and selecting K adjacent samples according to a K adjacent method;
(2) Calculating Euclidean distance d from K neighbor samples to test sample Q i I =1 \ 8230K, and obtaining a normalized distance d after normalization processing i '; and calculating a weighted average absolute value error:
wherein e ti The prediction error of the ith neighbor sample of the test sample Q for the tth base learning machine is T =1, \ 8230; and e ti ＝f ti -y i ，f ti Predicted value, y, for the ith base learning machine for the ith neighbor sample i The true output value of the ith neighbor sample;
(3) For the test sample Q, calculating a weight corresponding to the t-th base learning machine based on the weighted average absolute value error:
wherein Z is a normalization factor, such that
3. The method of claim 2, wherein the step of performing the integrated prediction comprises applying each of the base learning machines to the model by the following formulaPredicted result of (2)And (4) integrating to obtain a final prediction result:
wherein s is t As a result of prediction of the t-th base learning machine, w tQ Is the weight corresponding to the t-th base learning machine, K (·) is the kernel function, and h is the bandwidth.
4. The method for predicting the gas circuit parameters of the aeroengine based on the dynamic integrated algorithm according to any one of claims 1 to 3, wherein the iterative training step comprises the following iterative steps for the tth base learning machine:
(1) In the sample weight distribution of D t Training sample setTraining a tth base learning machine, wherein T =1, \8230, and T is the number of the base learning machines;
(2) Calculating the absolute value error predicted by the tth learning machine on the training sample to form the tth column of an absolute value error matrix E: e (j, t) = | ft (x) j )-y j |,j＝1,…M；f t (x j ) For the t-th base learning machine f t For the jth training sample x j Predicted result of (1), y j The real output value of the jth training sample;
(3) Calculating the t-th base learning machine f t Error rate of (2):
wherein phi is a preset threshold value of the absolute value of the relative error;
is provided withn is 1,2 or 3;
(4) Update the sample weight D t ：
Wherein Z t Is a normalization factor, such that
5. The aircraft engine gas circuit parameter prediction method based on the dynamic integration algorithm as claimed in any one of claims 1 to 3, wherein in the iterative training step, an iterative algorithm of Adaboost.R2 is adopted to learn the training sample set to obtain a base learning machine.
6. The utility model provides an aeroengine gas circuit parameter prediction system based on dynamic integration algorithm which characterized in that includes:
the iterative training module is used for learning the training sample set based on an iterative algorithm to obtain a base learning machine, and predicting the test sample set by using the base learning machine to obtain a prediction result of each base learning machine;
the weight determination module is used for selecting a neighbor sample of the test sample in the training sample set, evaluating the local performance of each base learning machine in the neighbor sample and dynamically determining the weight of each base learning machine;
and the integrated prediction module is used for integrating the prediction result of each base learning machine by utilizing weighted kernel density estimation based on the weight of each base learning machine to obtain a final prediction result.
7. The dynamically integrated algorithm based aircraft engine gas path parameter prediction system of claim 6, wherein the weight determination module comprises:
the neighbor sample selection unit is used for calculating the distances between all training samples and the test sample Q for the test sample Q, arranging the training samples in the order from small to large, and selecting K neighbor samples according to a K neighbor method;
an absolute value error calculation unit for calculating Euclidean distances d from the K neighbor samples to the test sample Q i I =1 \ 8230K, and obtaining a normalized distance d after normalization processing i '; and calculating a weighted average absolute value error:
wherein e ti The prediction error of the ith neighbor sample of the test sample Q for the tth base learning machine is T =1, \ 8230; and e ti ＝f ti -y i ，f ti Predicted value, y, for the ith base learning machine for the ith neighbor sample i The true output value of the ith neighbor sample;
and the weight calculation unit is used for calculating the weight corresponding to the tth base learning machine based on the weighted average absolute value error for the test sample Q:
wherein Z is a normalization factor, such that
8. The dynamically integrated algorithm-based aircraft engine gas circuit parameter prediction system of claim 7, wherein each base learning machine is identified in the integrated prediction module by the following formulaPredicted result of (2)And integrating to obtain a final prediction result:
wherein s is t As a result of prediction of the t-th base learning machine, w tQ Is the weight corresponding to the t-th base learning machine, K (-) is the kernel function, and h is the bandwidth.
9. The system according to any one of claims 6 to 8, wherein the iterative training module performs the following iterative steps for the tth base learning machine:
(1) In the sample weight distribution of D t Training sample setTraining a T-th base learning machine, wherein T =1, \8230, and T is the number of the base learning machines;
(2) Calculating the absolute value error predicted by the tth learning machine on the training sample to form the tth column of an absolute value error matrix E: e (j, t) = | f t (x j )-y j |,j＝1,…M；f t (x j ) For the tth base learning machine ft to the jth training sample x j Predicted result of (1), y j The real output value of the jth training sample;
(3) Calculating the t-th base learning machine f t Error rate of (2):
wherein phi is a preset threshold value of the absolute value of the relative error;
is provided withn is 1,2 or 3;
(4) Update the sample weight D t ：
Wherein Z t Is a normalization factor, makes
10. The system for predicting the air circuit parameters of the aircraft engine based on the dynamic integration algorithm according to any one of claims 7 to 8, wherein the iterative training module learns the training sample set by adopting an iterative algorithm of Adaboost.R2 to obtain a base learning machine.
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