An aero-engine residual life prediction method fusing machine learning and improved GM (1, N) model

Abstract

The present application relates to the field of aero-engine health management and residual life prediction, and discloses a residual life prediction method of aero-engine fusing machine learning and improved GM(1, N) model. The method faces aero-engine multi-source monitoring data, firstly, the working condition and sensor time sequence are preprocessed and feature construction is carried out; then, the adaptive window division is carried out on the operation sequence of a single engine, so that different stages are allowed to present different dynamic characteristics; further, the total life is introduced as a unified unknown quantity to construct the main variable of residual life, the grey modeling is established in each window, and the robust solution is carried out according to the relative error criterion, the total life estimation is obtained by searching, and the residual life prediction value is output; when the training data is available, the life estimation and fitting error output by the grey model are taken as additional features, which are fused with the original features and input into the machine learning model for integrated prediction, so as to form a solution for the residual life prediction of aero-engine.

Description

Technical Field

[0001] This invention relates to the field of aero-engine health management and life prediction technology, and in particular to a method for predicting the remaining life of aero-engines by integrating machine learning and an improved GM(1,N) model. Background Technology

[0002] As complex power equipment, aero engines experience continuous performance degradation over time due to their high-load and long-cycle operation. Failures directly threaten flight safety and incur high maintenance costs. Accurate prediction of their Remaining Useful Life (RUL) is a core technology for condition-based maintenance, requiring the construction of reliable predictive models based on multi-dimensional operating parameters and sensor monitoring data.

[0003] In existing technologies, RUL prediction methods for aero-engines can be divided into three categories: physical model-based methods require the establishment of complex degradation mechanism models, but are difficult to implement in engineering applications due to the complexity of engine structures and the coupling effect of multiple factors; data-driven methods rely on historical data to train prediction models, but have inherent defects such as high sensitivity to data quality and poor interpretability of black-box models; fusion methods attempt to combine the advantages of the first two types of methods, but still have the following technical bottlenecks:

[0004] Insufficient adaptability to degradation process: It fails to effectively capture the stage characteristics of engine degradation. When changes in operating conditions or cumulative damage cause abrupt changes in the degradation rate, the model parameters cannot be dynamically adjusted, resulting in a break in the continuity of prediction.

[0005] Target quantity estimation logic flaw: It ignores the essential attribute of RUL as "quantity to be estimated in the non-failure state", and in online prediction scenarios lacking complete failure labels, it is difficult to establish a mapping relationship between input features and remaining lifetime.

[0006] The search space design is fixed: it uses a fixed range of lifetime candidate sets, which cannot dynamically optimize the search interval according to the distribution of the training set, resulting in the prediction accuracy being limited by boundary conditions.

[0007] The feature fusion mechanism is weak: the combination of physical model and data-driven model is limited to simple weighting at the result level, without achieving deep fusion of degenerate features, and thus cannot balance prediction accuracy and engineering interpretability.

[0008] To address the aforementioned shortcomings, this invention proposes a prediction method that integrates machine learning and an improved GM(1,N) model. By constructing a dynamic search space, adapting features in multiple stages, and using a hybrid model architecture, this method overcomes the deficiencies of existing technologies in terms of adaptability to complex working conditions, stability of prediction accuracy, and feasibility of engineering deployment. Summary of the Invention

[0009] To address the shortcomings of existing technologies, this invention provides a method for predicting the remaining life of aero-engines by integrating machine learning and an improved GM(1,N) model. This method solves the problems of traditional methods, such as reliance on a fixed search range, inability to dynamically adapt to degradation stages, and weak feature fusion mechanisms. This invention improves prediction accuracy and stability through adaptive window partitioning, dynamic search space construction, and gray-machine learning feature-level fusion.

[0010] To address the aforementioned technical problems, this invention provides the following technical solution: a method for predicting the remaining life of an aero-engine by integrating machine learning and an improved GM(1,N) model, comprising the following steps:

[0011] By collecting multi-source operational data from aero-engines and performing cleaning, correlation analysis, and standardized preprocessing, standardized feature sequences are generated.

[0012] Based on the stability criterion of data variation, time series data is divided into several time windows to accurately and dynamically capture the degradation characteristics of the engine at different stages.

[0013] Using the unknown candidate total lifetime as the optimization variable, an improved GM(1,N) model is established for each window. The optimal parameter vector is solved by the relative absolute error fitting criterion, so as to realize the joint modeling of the remaining lifetime by multiple variables.

[0014] The search interval is dynamically adjusted based on the total lifetime sample distribution of the training set. The optimal total lifetime estimate is determined in the total lifetime candidate set, and the remaining lifetime prediction value at the current moment is directly output, forming an independent gray prediction capability.

[0015] The total lifetime estimate and corresponding global fitting error output by the improved GM(1,N) model are used as gray features, fused with the standardized feature sequence, and then input into the machine learning model. The prediction results are further optimized through data-driven methods to achieve synergy between the physical model and the data model.

[0016] Furthermore, generating the standardized feature sequence specifically includes the following steps:

[0017] Input the original multi-source operating data of the aero-engine, including at least the unit number, timestamp, operating parameters and sensor monitoring parameters. Convert the non-numerical operating parameters and sensor parameters into numerical ones, remove non-numerical outliers, remove operating parameters and sensor parameters with constant values, and obtain the time series and corresponding multivariate observation series of each engine.

[0018] Let the candidate feature set be the set of all feature variables. Calculate the Pearson correlation coefficient between any two feature variables and remove redundant variables whose absolute value of the correlation coefficient is greater than a preset threshold in order to reduce multicollinearity.

[0019] Z-score standardization is performed on the feature set after removing redundant variables from each dimension after screening to obtain a standardized feature sequence, thus eliminating the dimensional differences between different features.

[0020] Furthermore, accurately and dynamically capturing the degradation characteristics of the engine at different stages specifically includes the following steps:

[0021] Input the multivariate observation sequence of each engine obtained after processing and the total number of variables N, set the minimum window length, and ensure that the number of sampling points in each window is not less than the total number of variables N;

[0022] Starting from the beginning of the engine time-series data, the window is expanded point by point, and the degree of variation index of each sampling point within the current window is calculated in real time. When the indicator fluctuation exceeds the preset stability threshold, the expansion stops and the current window is formed. The specific judgment formula is as follows:

[0023] ;

[0024] Then, using the end point of the current window as the starting point of the next window, the adaptive window expansion step is repeated until all windows completely cover the entire observation sequence of the engine, and the time series division results of multi-stage degradation features of several time windows are output.

[0025] Furthermore, using the unknown candidate total lifetime as the optimization variable, an improved GM(1,N) model is established for each window. The specific process of solving for the optimal parameter vector through the relative absolute error fitting criterion includes the following steps:

[0026] The input is divided into w-th time windows. A sampling time sequence Introducing unknown engine candidate total life As a unified unknown to be estimated, for the th Within a window The sampling point is used to construct the nth sampling point. The zero-order sequence of the remaining lifetime main variable within each window is:

[0027] ;

[0028] The zero-order sequence of the remaining lifespan main variable and the observed sequence of the influencing variables from the measured data are processed by generating a cumulative sequence. Then, the background neighbor mean of the cumulative sequence of the remaining lifespan main variable is calculated. An improved GM(1,N) model containing the development coefficient and the driving coefficient is constructed and transformed into a matrix equation in the form of linear regression. The development coefficient reflects the rate of change of remaining lifespan, and the driving coefficient quantifies the correlation strength between each influencing variable and remaining lifespan.

[0029] The first The zero-order sequence of the remaining lifespan main variable within each window is used as the observation vector of the improved GM(1,N) model. , will the The background neighbor mean of the cumulative sequence of the main variables within each window and the cumulative sequence of the influencing variables from the measured data are used as the design matrix for the improved GM(1,N) model. The development coefficient and driving coefficient are used as the first The vector of parameters to be estimated in the improved GM(1,N) model within a window. This enables joint modeling of the remaining lifetime using multiple variables, resulting in a matrix equation: ;

[0030] Fixed candidate total lifetime and window To avoid the impact of base differences caused by different candidate total lifetimes, the relative absolute error is used as the fitting criterion to construct the objective function. The parameter vector of the improved GM(1,N) model is then solved, defined as:

[0031] ;

[0032] ;

[0033] in, , For the first The number of valid sampling points within a time window The minimum positive number is preset. For the first Within a window, the relative absolute error of the improved GM(1,N) model is calculated. Since the objective function is not differentiable, the model parameters are solved using the iterative reweighted least squares method (MM / IRLS), i.e., the method for solving weighted least squares problems. By minimizing the upper bound, the iteration ensures that the relative absolute error does not increase monotonically, thus obtaining the optimal parameter vector for model stability. .

[0034] Furthermore, constrain the total lifetime of candidates. The lower bound of the feasible region is the maximum operating time observed in all windows of the engine, ensuring that the remaining lifetime is non-negative.

[0035] Furthermore, the specific process of dynamically adjusting the search interval based on the total lifetime sample distribution of the training set includes the following steps:

[0036] Calculate the lower quartile Q1, upper quartile Q3, and interquartile range IQR = Q3 - Q1 for each engine total lifespan sample in the training set, based on a preset constant. Through formula and Theoretical lower bound for determining the search range of candidate total lifetime values and theoretical upper limit ;

[0037] The lower bound of the theory and theoretical upper limit Each is constrained by the minimum of the total lifetime of the training set. With the maximum value Between, the lower bound is constrained. and constrained upper bound ;

[0038] For the engine to be predicted, find the minimum value of its total lifespan candidate set. Set to be no less than the current observed maximum runtime + 1, and satisfy the following conditions: This ultimately forms the candidate set for total lifetime. .

[0039] Furthermore, the specific process of determining the optimal total lifetime estimate from the candidate total lifetime set and directly outputting the predicted remaining lifetime value at the current moment includes the following steps:

[0040] In the total lifetime candidate set When searching, for each candidate total lifetime , in each time window The optimal parameter vector of the model obtained through the IRLS method The global fitting error is obtained by summing the corresponding relative and absolute errors. Then, the optimal total life estimate is determined by minimizing the global fitting error of multiple windows for the same engine. ;

[0041] Based on the optimal total lifetime estimate Calculate the remaining lifetime prediction at the current moment based on the current running time: ;

[0042] in, This represents the running time or the number of loops at the current moment.

[0043] Furthermore, the total lifetime estimate and corresponding global fitting error output by the improved GM(1,N) model are used as gray features, fused with the standardized feature sequence, and then input into the machine learning model. The specific steps for further optimizing the prediction results through data-driven methods include:

[0044] Construct a fusion feature vector, which includes the original feature sequence output from the data preprocessing stage, the optimal total lifetime estimate, and the corresponding global fitting error;

[0045] The training set of complete engine life cycle data and the fused feature vector are used as input features of the machine learning model. The training set is randomly truncated multiple times to generate multiple partial life cycle input samples. Each partial life cycle input sample contains all the running data from the start of engine operation to the random truncation time. Each partial life cycle input sample is also set with a remaining life cycle label, which is the remaining running time from the truncation time to the engine failure time.

[0046] Using the unit number as the grouping basis, the machine learning model is trained by grouped cross-validation to optimize the model parameters and evaluate the generalization ability of the model at different running stages, so as to obtain the trained machine learning model.

[0047] The test set engine operation data is input into the trained machine learning model. The root mean square error (RMSE) and its standard deviation stability index are used as comprehensive evaluation criteria to select the optimal machine learning model. For each type of model, the top K sub-models with the best cross-validation performance are retained. During prediction, the ensemble prediction result is obtained by averaging the outputs of the top K sub-models. Finally, the remaining life prediction value of the fused machine learning model is obtained.

[0048] Furthermore, the present invention also provides an aero-engine remaining life prediction device, comprising: a data preprocessing module, an adaptive window partitioning module, an unknown total life joint estimation grey modeling module, a remaining life search optimization module, and an improved GM(1,N) model and machine learning fusion module, each module being used to execute the method steps described in any of the above embodiments, wherein:

[0049] The data preprocessing module is used to generate standardized feature sequences by collecting multi-source operating data of aero-engines and performing cleaning, correlation analysis and standardization preprocessing.

[0050] The adaptive window partitioning module is used to divide time series data into several time windows based on the stability criterion of data variation, so as to accurately and dynamically capture the degradation characteristics of the engine at different stages.

[0051] The gray modeling module for joint estimation of unknown total lifetime is used to establish an improved GM(1,N) model for each window with unknown candidate total lifetime as the optimization variable, and solve the optimal parameter vector through the relative absolute error fitting criterion to realize the joint modeling of multiple variables on the remaining lifetime.

[0052] The remaining lifetime search optimization module is used to dynamically adjust the search interval based on the total lifetime sample distribution in the training set, determine the optimal total lifetime estimate in the total lifetime candidate set, and directly output the remaining lifetime prediction value at the current moment, forming an independent gray prediction capability.

[0053] An improved GM(1,N) model and machine learning fusion module is used to take the total lifetime estimate and corresponding global fitting error output by the improved GM(1,N) model as gray features, fuse them with the standardized feature sequence, and input them into the machine learning model. The prediction results are further optimized through data-driven methods to achieve synergy between the physical model and the data model.

[0054] Furthermore, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in any of the preceding claims.

[0055] By employing the above technical solutions, this invention provides a method for predicting the remaining life of aero-engines by integrating machine learning and an improved GM(1,N) model. Through adaptive window partitioning, dynamic search space construction, and grey-machine learning feature-level fusion, the following beneficial effects are achieved:

[0056] This invention significantly reduces prediction errors and improves prediction accuracy under complex working conditions by capturing phased degradation features; the dynamic search space design effectively reduces dependence on boundary conditions and enhances the engineering adaptability of the model; the optimized feature fusion mechanism achieves a synergistic improvement in the interpretability of the physical model and the generalization ability of the data-driven model; and the application scenario coverage is expanded to support online prediction scenarios without complete failure labels, with the stability index of the prediction results controlled within an acceptable range for engineering. Attached Figure Description

[0057] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0058] Figure 1 This is a schematic diagram of the method flow proposed in this invention;

[0059] Figure 2 This is a schematic diagram illustrating the lifetime search and prediction results under empirical prediction scenarios.

[0060] Figure 3 A diagram showing the comparison of the mean RMSE of various machine learning models under 50 random truncation cycles;

[0061] Figure 4 A diagram showing the RMSE stability comparison of various machine learning models under 50 random truncation cycles;

[0062] Figure 5 This is a diagram comparing the prediction results of various machine learning models on the test data.

[0063] Figure 6 This is a schematic diagram illustrating the overall fitting effect of the optimal fusion model. Detailed Implementation

[0064] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0065] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0066] Please refer to Figures 1-6 This illustrates a specific implementation of the present embodiment. This embodiment achieves the effect of improving prediction accuracy and stability through adaptive window partitioning, dynamic search space construction, and gray-machine learning feature-level fusion.

[0067] Please refer to Figure 1 This embodiment proposes a method for predicting the remaining life of aero-engines by integrating machine learning and an improved GM(1,N) model. The method includes the following steps:

[0068] S1. Data Preprocessing: By collecting multi-source operational data of aero-engines and performing cleaning, correlation analysis and standardization preprocessing, a standardized feature sequence is generated.

[0069] As a preferred embodiment of step S1, step S1 includes the following sub-steps:

[0070] Input the original multi-source operating data of the aero-engine, including at least the unit number, timestamp, operating parameters and sensor monitoring parameters. Convert the non-numerical operating parameters and sensor parameters into numerical ones, remove non-numerical outliers, remove operating parameters and sensor parameters with constant values, and obtain the time series and corresponding multivariate observation series of each engine.

[0071] Let the candidate feature set be the set of all feature variables. Calculate any two feature variables and Pearson correlation coefficient between them:

[0072] ;

[0073] like If the threshold is exceeded, redundant variables are removed to reduce multicollinearity and simplify the model, provided that more information or lifespan is retained.

[0074] Z-score standardization is performed on the feature set after removing redundant variables from each dimension after screening to obtain a standardized feature sequence, thus eliminating the dimensional differences between different features.

[0075] Specifically, the standardized formula is: ;

[0076] in, For the original feature variables in the th The observations at each sampling time point, This represents the mean of the characteristic variables in the same engine sample. The standard deviation of the characteristic variables in the same engine sample; These are the feature values ​​after Z-score standardization.

[0077] S2. Adaptive window partitioning enables dynamic feature capture: Based on the stability criterion of data variation, time series data is divided into several time windows to accurately and dynamically capture the degradation characteristics of the engine at different stages; adaptive window partitioning provides more accurate input data for subsequent "grey modeling of joint estimation of unknown total life".

[0078] As a preferred embodiment of step S2, step S2 includes the following sub-steps:

[0079] Input the multivariate observation sequence of each engine and the total number of variables N obtained after processing in step S1, set the minimum window length, and ensure that the number of sampling points in each window is not less than the total number of variables N to ensure the effectiveness of modeling;

[0080] Starting from the beginning of the engine time-series data, the window is expanded point by point, and the degree of variation index of each sampling point within the current window is calculated in real time. When the indicator fluctuation exceeds the preset stability threshold The expansion stops and the current window is formed when the time is right. The specific formula for determining this is:

[0081] ;

[0082] Where the threshold Take 0.3;

[0083] Then, using the end point of the current window as the starting point of the next window, the adaptive window expansion step is repeated until all windows completely cover the entire observation sequence of the engine, and the time series division results of multi-stage degradation features of several time windows are output.

[0084] Traditional methods fail to effectively capture the phased characteristics of engine degradation. When changes in operating conditions or accumulated damage cause abrupt changes in the degradation rate, the model parameters cannot be dynamically adjusted, resulting in interruptions in prediction continuity. This embodiment uses adaptive windowing to dynamically capture phased degradation characteristics. The window is expanded point by point from the starting point of the engine time series data, and the degree of variation index of each sampling point within the window is calculated in real time. When the index fluctuation exceeds the preset stability threshold, the expansion stops and the current window is formed. The end point of the window is then used as the starting point of the next window until the entire observation sequence is covered. By dividing the entire life cycle into several time windows that meet the stability requirements, the model can adapt to the characteristics of different degradation stages and avoid interruptions in prediction continuity caused by changes in operating conditions or accumulated damage.

[0085] S3. Improved GM(1,N) model construction and parameter optimization: Using the unknown candidate total lifetime as the optimization variable, an improved GM(1,N) model is established for each window. The optimal parameter vector is solved by the relative absolute error fitting criterion, so as to realize the joint modeling of the remaining lifetime by multiple variables.

[0086] As a preferred embodiment of step S3, step S3 includes the following sub-steps:

[0087] The input is divided into w-th time windows. A sampling time sequence (Running time or number of cycles), introducing an unknown candidate total engine life. As a unified unknown to be estimated, for the th Within each window The nth sampling point is used to construct the nth sampling point. The 0th-order sequence of the remaining lifetime main variable within each window is:

[0088] ;

[0089] Specifically, constrain the total lifetime of candidates The lower bound of the feasible region is the maximum operating time observed in all windows of the engine, ensuring that the remaining lifetime definition does not have a negative value, i.e., the candidate total lifetime. The feasible region satisfies:

[0090] ;

[0091] For any variable (Including main variables) and influencing variables Define a sequence generated by a single accumulation:

[0092] ;

[0093] And calculate the main variables The 1-AGO sequence defines the background value (neighbor mean):

[0094] ;

[0095] Among them, due to rely ,therefore and It also depends on y; influencing variables Based on actual test data, not dependent on ;

[0096] Constructing a system that includes a development coefficient and driving coefficient Improved GM(1,N) model:

[0097] ;

[0098] in, The main variable representing remaining lifespan is the first... The first window A sequence of (1-AGO) is generated by the cumulative summation of 1 variable. This represents the background value (neighbor mean) of the 1-AGO sequence of the main variable, used to improve the construction of the GM(1,N) model; Indicates the first The evolution coefficients of the improved GM(1,N) model within a window reflect the rate of change of the main variables; Indicates the first The first window The driving coefficients of each influencing variable are used to quantify the strength of the association between each influencing variable and remaining lifespan.

[0099] And transform it into a matrix equation of linear regression form:

[0100] ;

[0101] The first The zero-order sequence of the remaining lifetime main variable within each window is used as the observation vector for the improved GM(1,N) model:

[0102] ;

[0103] The first The background neighbor mean of the cumulative sequence of the main variables within each window and the cumulative sequence of the influencing variables from the measured data are used as the design matrix for the improved GM(1,N) model. Integrating background values ​​and influencing variable information:

[0104] ;

[0105] The development coefficient and driving coefficient are used as the first The vector of parameters to be estimated for the improved GM(1,N) model within a window:

[0106] ;

[0107] This enables joint modeling of the remaining lifetime by multiple variables, resulting in the matrix equation: ;

[0108] Fixed candidate total lifetime and window To avoid the impact of base differences caused by different candidate total lifetimes, the relative-absolute error (relative-L1) is used as the fitting criterion to construct the objective function. The parameter vector of the improved GM(1,N) model is solved, defined as:

[0109] ;

[0110] in, , For the first The number of valid sampling points within a time window The minimum positive number is preset. For the first The relative absolute error of the improved GM(1,N) model within a window is determined; since the objective function is not differentiable, the model parameters are solved using the iterative reweighted least squares method MM / IRLS, i.e., the solution method for weighted least squares problems, at the nth window. Construct a weighted least squares subproblem in the next iteration:

[0111] ;

[0112] in, , For the first The number of valid sampling points within a time window This is the observation vector. Denotes the coefficient vector to be estimated, where Inside These are the optimization variables for this problem and will change during the solution process; It is the first The parameter estimate obtained in the next iteration is from the previous round.

[0113] By applying the principle of minimizing the upper bound, iteration ensures that the relative absolute error does not increase monotonically, thus obtaining the optimal parameter vector for model stability. .

[0114] Traditional methods neglect the essential attribute of RUL as "a quantity to be estimated in the non-failure state". In online prediction scenarios lacking complete failure labels, it is difficult to establish a mapping relationship between input features and remaining lifetime. In this embodiment, in online scenarios lacking complete failure labels, the remaining lifetime is indirectly derived by estimating the total lifetime, thus establishing a mapping relationship between input features and RUL.

[0115] S4. Total lifetime search optimization output preliminary prediction: The search interval is dynamically adjusted based on the total lifetime sample distribution in the training set. The optimal total lifetime estimate is determined in the total lifetime candidate set, and the remaining lifetime prediction value at the current moment is directly output, forming an independent gray prediction capability.

[0116] In a preferred embodiment of step S4, step S4 includes:

[0117] Candidate sets are determined by the total lifetime distribution of the training data. The upper and lower bounds are as follows: Let the first training set be... The actual total lifespan sample of the engine is ,but

[0118] ;

[0119] ;

[0120] Based on preset constants ,Pick Through formula and Theoretical lower bound for determining the search range of candidate total lifetime values and theoretical upper limit ;

[0121] The lower bound of the theory and theoretical upper limit Each is constrained by the minimum of the total lifetime of the training set. With the maximum value Between, the lower bound is constrained. and constrained upper bound ;

[0122] For the engine to be predicted, find the minimum value of its total lifespan candidate set. Set to be no less than the current observed maximum runtime + 1, and satisfy the following conditions: This ultimately forms the candidate set for total lifetime. .

[0123] In the total lifetime candidate set When searching, for each candidate total lifetime , in each time window The optimal parameter vector of the model obtained through the IRLS method The global fitting error is obtained by summing the corresponding relative and absolute errors. ;

[0124] ;

[0125] Indicates the first The optimal total lifespan estimate is obtained by minimizing the global fitting error across multiple windows of the same engine, using the number of valid sampling points within each time window. ;

[0126] Based on the optimal total lifetime estimate Calculate the remaining lifetime prediction at the current moment based on the current running time: ;

[0127] in, This represents the running time or the number of loops at the current moment.

[0128] Traditional methods use a fixed range of lifetime candidate sets, which cannot dynamically optimize the search interval according to the distribution of the training set, resulting in prediction accuracy being limited by boundary conditions. This embodiment dynamically optimizes the search interval based on the total lifetime sample distribution of the training set, and searches for the optimal total lifetime estimate by minimizing the global fitting error of the multi-window method, avoiding the accuracy limitation caused by fixed boundaries, making the search range adapt to the distribution of training data, and improving prediction robustness.

[0129] S5. Feature fusion improves prediction accuracy: The total lifetime estimate and corresponding global fitting error output by the improved GM(1,N) model are used as gray features and fused with the standardized feature sequence before being input into the machine learning model. The prediction results are further optimized through data-driven methods to achieve synergistic optimization of the physical model and the data model. The fusion of the improved GM(1,N) model and machine learning combines the advantages of the physical model and the data model, improving prediction accuracy and stability. The first four steps constitute an independent gray prediction link. The fifth step introduces machine learning through feature fusion, forming a two-layer architecture of basic prediction and accuracy improvement. This ensures availability when there is no training data and enhances prediction performance under complex conditions through the fusion mechanism.

[0130] As a preferred embodiment of step S5, step S5 includes:

[0131] Constructing fused feature vectors The fused feature vector contains the original feature sequence output from the data preprocessing stage. Optimal total lifetime estimate and the corresponding global fitting error ;

[0132] The training set of complete engine life cycle data and the fused feature vector are used as input features of the machine learning model. The training set is randomly truncated multiple times to generate multiple partial life cycle input samples. Each partial life cycle input sample contains all the running data from the start of engine operation to the random truncation time. Each partial life cycle input sample is also set with a remaining life cycle label, which is the remaining running time from the truncation time to the engine failure time.

[0133] Using the unit number as the grouping basis, the machine learning model is trained by grouped cross-validation to optimize the model parameters and evaluate the generalization ability of the model at different running stages, so as to obtain the trained machine learning model.

[0134] The test set engine operation data is input into the trained machine learning model. The root mean square error (RMSE) and its standard deviation stability index are used as comprehensive evaluation criteria to select the optimal machine learning model. For each type of model, the top K sub-models with the best cross-validation effect are retained. During prediction, the ensemble prediction result is obtained by taking the average of the outputs of the top K sub-models. Finally, the remaining life prediction value of the fused machine learning model is obtained, which breaks through the limitation of simple weighting at the result level and realizes the feature-level fusion of physical model (improved GM(1,N) model) and data-driven model (machine learning), taking into account both prediction accuracy and engineering interpretability.

[0135] Where, let the number of test samples be... , No. The true remaining lifetime value of each test sample is , No. The predicted remaining lifetime value for each test sample is The mean absolute error reflects the overall degree of deviation in the prediction results. The root mean square error, which measures the accuracy of prediction, is as follows:

[0136] ;

[0137] Let's assume a total of The root mean square error obtained from the c-th random truncation cycle is: This reflects the mean RMSE over multiple iterations, indicating the model's average accuracy. and the standard deviation of RMSE over multiple cycles, reflecting the stability of the model. They are respectively:

[0138] ;

[0139] .

[0140] Traditional methods that combine physical models and data-driven models only perform simple weighting at the result level, failing to achieve deep fusion of degenerate features and thus failing to balance prediction accuracy and engineering interpretability. This embodiment constructs a deep fusion model of gray features and original features, and integrates machine learning for prediction, breaking through the limitations of simple weighting at the result level. It achieves feature-level fusion of the physical model (gray model) and the data-driven model (machine learning), balancing prediction accuracy and engineering interpretability.

[0141] It should be noted that the data in this invention comes from NASA's C-MAPSS turbofan engine degradation simulation dataset. This dataset includes a training set and a test set: the training set records the complete cycle of the engine from normal operation to failure, while the test set only contains a partial sequence up to a certain point in time before the failure, and provides a file of the actual remaining life of the test set for evaluation. Both the training and test files have 26 columns, which include, in order: cell number, time, three types of operating conditions (flight altitude, Mach number, and throttle lever angle), and output signals from 21 sensors. The specific parameter meanings of the 21 sensor output signals are shown in Table 1.

[0142] Table 1. Meaning of Sensor Data

[0143]

[0144] After multicollinearity analysis and removal of constant parameters, this embodiment ultimately retains the following variables as inputs: cell number, time, flight altitude, Mach number, T24, T30, NRF, NRC, W31, and W32; and standardizes the above variables to eliminate the influence of dimensional differences on modeling and learning.

[0145] In scenarios where no training data is available, the improved GM(1,N) model can predict the total lifespan of the device model based solely on historical experience and its upper and lower bounds. Specifically, in this embodiment, the upper bound of the search for the total lifespan of the device model is set to 300, and the lower bound to 100, based on historical experience. Within this search range, the standardized variables are used as input, and the improved grey prediction method is directly applied to 100 devices to obtain the remaining lifespan prediction results as follows. Figure 2 As shown in the figure. In this case, the prediction accuracy is evaluated as follows: the stability index MAE is 35 days and the root mean square error RMSE is 45 days. Experimental results show that, without relying on training data, this method can still output prediction results that have a consistent trend with the actual remaining lifetime, thus verifying the feasibility and engineering applicability of the method.

[0146] In scenarios where training data is known, the aforementioned variables are initially used as basic input features in the machine learning phase. In the fusion learning phase, gray features obtained from improved gray modeling are further introduced on top of these basic features, including the "preliminary prediction of total lifetime." and the corresponding fitting error This results in a fusion of feature inputs, which enhances the model's ability to represent the degradation process.

[0147] To evaluate the accuracy and stability of the prediction results, this embodiment uses the mean absolute error (MAE) and root mean square error (RMSE) as accuracy indicators; simultaneously, in multiple randomized cyclic experiments, the standard deviation of RMSE in the cyclic dimension is used. Characterizes stability, used to describe the degree of fluctuation in the model's output.

[0148] In the specific training process, this embodiment first uses the quartile method to determine the upper and lower bounds of the total lifetime search range based on the true total lifetime distribution of the training samples; then, it randomly extracts the first 1 to 1200 training samples from each training device. Using the operational data, within the defined search range, an improved grey prediction method is executed to obtain the "preliminary prediction value of total lifetime" corresponding to the truncated sample. "and fitting error" Then As fusion input, eight machine learning models were trained and cross-validated. Then, the random truncation and training process was repeated 50 times to obtain the statistical performance of each model in terms of accuracy and stability.

[0149] To facilitate engineering deployment and reduce random fluctuations caused by single segmentation, this embodiment retains the top 5 sub-models with the best cross-validation performance for each type of model in each loop. When predicting new test data, the prediction results of these top 5 sub-models are output separately and averaged as the final output of the model, thereby achieving a more stable integrated prediction effect.

[0150] Figure 3 A diagram showing the comparison of the mean RMSE of various machine learning models under 50 random truncation cycles; Figure 4 This is a diagram comparing the RMSE stability of various machine learning models under 50 random truncation cycles; the machine learning models include:

[0151] 1. LightGBM (Light Gradient Boosting Machine)

[0152] 2. SVR_RBF (Support Vector Regression with Radial Basis Function kernel)

[0153] 3. CatBoost (Categorical Boosting, a gradient boosting algorithm for categorical features)

[0154] 4. HGBDT (Histogram-based Gradient Boosting Decision Tree)

[0155] 5. GBDT (Gradient Boosting Decision Tree)

[0156] 6. RandomForest

[0157] 7. XGBoost (Extreme Gradient Boosting)

[0158] 8. ExtraTrees (Extremely Randomized Trees)

[0159] By comparing the overall performance of "GM features without the improved GM(1,N) model" and "GM features with the improved GM(1,N) model" under 50 randomized partitioning cycles, the following statistical conclusions can be drawn: Overall, RMSE The mean decreased from 40.2665 to 39.2996 (a decrease of 0.9670, an increase of 2.40%); RMSE The std value decreased from 6.7936 to 6.0982 (a decrease of 0.6954, or an improvement of 10.24%). The results show that after introducing the improved GM(1,N) model features, the model not only improved in terms of mean error but also enhanced in terms of stability. For detailed comparison results, please refer to [link to relevant comparisons]. Figure 3 , Figure 4 As shown.

[0160] After selecting the model from the training data, this embodiment further introduces new test data for validation. This test data also comes from 100 devices, but their actual remaining lifetime is unknown. To ensure fairness in the comparison, all models, except for the addition of new input features (improved GM(1,N) model features), maintain the same parameter settings and modeling methods. The comparison results are as follows: Figure 5As shown in the figure. From the overall evaluation metrics, the model performance improved after introducing the improved GM(1,N) model features: MAE decreased from 23.5234 to 22.6962, a reduction of 0.8272, representing an improvement of 3.52%; RMSE decreased from 31.6288 to 30.5480, a reduction of 1.0807, representing an improvement of 3.42%. The results indicate that adding the improved GM(1,N) model features can further improve the prediction accuracy of each model on the test data, resulting in a significant improvement in prediction performance.

[0161] Multiple iterations of the training data comparison show that, regardless of whether improved GM(1,N) model features are introduced, ExtraTrees consistently delivers the best prediction performance; on the test data, ExtraTrees also maintains its top position. Its key metrics after introducing improved GM(1,N) model features are: RMSE of 28.627 and MAE of 21.128 days; the corresponding overall fitting performance is as follows: Figure 6 As shown, the trend of the predicted values ​​and the true values ​​is basically consistent, indicating that the model can capture the degradation trend of the remaining life of the aero-engine. The model's fitting effect meets the requirements of engineering applications, especially in terms of adaptability and prediction accuracy under complex operating conditions. Therefore, the method of "improved GM(1,N) model features + machine learning fusion" proposed in this embodiment can further improve prediction accuracy and enhance the stability of results while maintaining interpretability.

[0162] In summary, this embodiment verifies that the method proposed in this invention can work under two types of application conditions: First, when only the empirical boundary of total lifetime is provided and training data is lacking, the remaining lifetime can still be predicted directly and usable results can be obtained; Second, when training data is available, the search range is determined based on the training data and the feature output of the improved GM(1,N) model is used as the fusion feature input to the machine learning model, which can further improve the prediction accuracy and stability on the test data.

[0163] Specifically, the present invention also provides an aero-engine remaining life prediction device, comprising: a data preprocessing module, an adaptive window partitioning module, an unknown total life joint estimation grey modeling module, a remaining life search optimization module, and an improved GM(1,N) model and machine learning fusion module. Each module is used to execute the above-mentioned method steps, wherein:

[0164] The data preprocessing module is used to generate standardized feature sequences by collecting multi-source operating data of aero-engines and performing cleaning, correlation analysis and standardization preprocessing.

[0165] The adaptive window partitioning module is used to divide time series data into several time windows based on the stability criterion of data variation, so as to accurately and dynamically capture the degradation characteristics of the engine at different stages.

[0166] The gray modeling module for joint estimation of unknown total lifetime is used to establish an improved GM(1,N) model for each window with unknown candidate total lifetime as the optimization variable, and solve the optimal parameter vector through the relative absolute error fitting criterion to realize the joint modeling of multiple variables on the remaining lifetime.

[0167] The remaining lifetime search optimization module is used to dynamically adjust the search interval based on the total lifetime sample distribution in the training set, determine the optimal total lifetime estimate in the total lifetime candidate set, and directly output the remaining lifetime prediction value at the current moment, forming an independent gray prediction capability.

[0168] An improved GM(1,N) model and machine learning fusion module is used to take the total lifetime estimate and corresponding global fitting error output by the improved GM(1,N) model as gray features, fuse them with the standardized feature sequence, and input them into the machine learning model. The prediction results are further optimized through data-driven methods to achieve synergy between the physical model and the data model.

[0169] In this specification, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to at least one embodiment or example described in connection with a specific feature, structure, material, or characteristic. These specific features, structures, materials, or characteristics may be combined in a suitable manner in one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples and their features described in this specification.

[0170] The logic and / or steps shown in the flowchart or otherwise described can be viewed as a sequence of executable instructions for implementing logical functions. These instructions may be implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device. Such systems, apparatus, or devices include processor systems or other systems capable of receiving and executing instructions.

[0171] The above embodiments detail the principles and implementation methods of the present invention, and illustrate its working principle using specific examples. These examples are only used to help understand the method and core ideas of the present invention. Furthermore, based on the ideas of the present invention, actual implementation methods and application scope may vary. Therefore, the content of this specification should not be construed as limiting the present invention.

Claims

1. A method for predicting the remaining life of an aero-engine by integrating machine learning and an improved GM(1,N) model, characterized in that, Includes the following steps: By collecting multi-source operational data from aero-engines and performing cleaning, correlation analysis, and standardized preprocessing, standardized feature sequences are generated. Based on the stability criterion of data variation, time series data is divided into several time windows to accurately and dynamically capture the degradation characteristics of the engine at different stages. Using the unknown candidate total lifetime as the optimization variable, an improved GM(1,N) model is established for each window. The optimal parameter vector is solved using the relative absolute error fitting criterion, achieving joint modeling of the remaining lifetime by multiple variables; specifically including: The input is divided into w-th time windows. A sampling time sequence Introducing unknown candidate total engine life As a unified unknown to be estimated, for the th Within each window The nth sampling point is used to construct the nth sampling point. The zero-order sequence of the remaining lifetime main variable within each window; The zero-order sequence of the remaining lifespan main variable and the observed sequence of the influencing variables from the measured data are processed by generating a cumulative sequence. Then, the background neighbor mean of the cumulative sequence of the remaining lifespan main variable is calculated. An improved GM(1,N) model containing the development coefficient and the driving coefficient is constructed and transformed into a matrix equation in the form of linear regression. The development coefficient reflects the rate of change of remaining lifespan, and the driving coefficient quantifies the correlation strength between each influencing variable and remaining lifespan. The first The zero-order sequence of the remaining lifespan main variable within each window is used as the observation vector of the improved GM(1,N) model. , will the The background neighbor mean of the cumulative sequence of the main variables within each window and the cumulative sequence of the influencing variables from the measured data are used as the design matrix for the improved GM(1,N) model. The development coefficient and driving coefficient are used as the first The vector of parameters to be estimated in the improved GM(1,N) model within a window. This enables joint modeling of the remaining lifetime by multiple variables, thereby obtaining a matrix equation; Fixed candidate total lifetime and window At this point, the relative absolute error is used as the fitting criterion to construct the objective function. Since this objective function is not differentiable, the model parameters are solved using the iterative reweighted least squares method, i.e., the method for solving weighted least squares problems. By minimizing the upper bound, the iteration is made so that the relative absolute error does not increase monotonically, thus obtaining the optimal parameter vector that stabilizes the model. ; The search interval is dynamically adjusted based on the total lifetime sample distribution of the training set. The optimal total lifetime estimate is determined in the total lifetime candidate set, and the remaining lifetime prediction value at the current moment is directly output, forming an independent gray prediction capability. The total lifetime estimate and corresponding global fitting error output by the improved GM(1,N) model are used as gray features, fused with the standardized feature sequence, and then input into the machine learning model. The prediction results are further optimized through data-driven methods to achieve synergy between the physical model and the data model.

2. The method for predicting the remaining life of aero-engines by integrating machine learning and an improved GM(1,N) model according to claim 1, characterized in that: Generating a standardized feature sequence specifically includes the following steps: Input the original multi-source operating data of the aero-engine, including at least the unit number, timestamp, operating parameters and sensor monitoring parameters. Convert the non-numerical operating parameters and sensor parameters into numerical ones, remove non-numerical outliers, remove operating parameters and sensor parameters with constant values, and obtain the time series and corresponding multivariate observation series of each engine. Let the candidate feature set be the set of all feature variables. Calculate the Pearson correlation coefficient between any two feature variables and remove redundant variables whose absolute value of the correlation coefficient is greater than a preset threshold in order to reduce multicollinearity. Z-score standardization is performed on the feature set after removing redundant variables from each dimension after screening to obtain a standardized feature sequence, thus eliminating the dimensional differences between different features.

3. The method for predicting the remaining life of an aero-engine by integrating machine learning and an improved GM(1,N) model according to claim 1, characterized in that: Based on the stability criterion of data variation, time-series data is divided into several time windows to accurately and dynamically capture the degradation characteristics of the engine at different stages. Specifically, this includes the following steps: Input the multivariate observation sequence of each engine obtained after processing and the total number of variables N, set the minimum window length, and ensure that the number of sampling points in each window is not less than the total number of variables N; Starting from the beginning of the engine time-series data, the window is expanded point by point, and the degree of variation index of each sampling point within the current window is calculated in real time. When the indicator fluctuation exceeds the preset stability threshold, the expansion stops and the current window is formed. The specific judgment formula is as follows: ； Then, using the end point of the current window as the starting point of the next window, the adaptive window expansion step is repeated until all windows completely cover the entire observation sequence of the engine, and the time series division results of multi-stage degradation features of several time windows are output.

4. The method for predicting the remaining life of an aero-engine by integrating machine learning and an improved GM(1,N) model according to claim 1, characterized in that: No. The zero-order sequence of the remaining lifetime main variable within each window is: ； The matrix equation of the improved GM(1,N) model is as follows: ; To avoid the impact of differences in baseline due to different candidate total lifetimes, relative absolute error is used as the fitting criterion to construct the objective function. The parameter vector of the improved GM(1,N) model is solved, defined as: ； ； in, , For the first The number of valid sampling points within a time window The minimum positive number is preset. For the first The relative absolute error of the improved GM(1,N) model within a window.

5. The method for predicting the remaining life of an aero-engine by integrating machine learning and an improved GM(1,N) model according to claim 4, characterized in that: Constraint candidate total lifetime The lower bound of the feasible region is the maximum operating time observed in all windows of the engine, ensuring that the remaining lifetime is non-negative.

6. The method for predicting the remaining life of an aero-engine by integrating machine learning and an improved GM(1,N) model according to claim 4, characterized in that: The specific process of dynamically adjusting the search interval based on the total lifetime sample distribution of the training set includes the following steps: Calculate the lower quartile Q1, upper quartile Q3, and interquartile range IQR = Q3 - Q1 for each engine total lifespan sample in the training set, based on a preset constant. Through formula and Theoretical lower bound for determining the search range of candidate total lifetime values and theoretical upper limit ; The lower bound of the theory and theoretical upper limit Each is constrained by the minimum of the total lifetime of the training set. With the maximum value Between, the lower bound is constrained. and constrained upper bound ; For the engine to be predicted, find the minimum value of its total lifespan candidate set. Set to be no less than the current observed maximum runtime + 1, and satisfy the following conditions: This ultimately forms the candidate set for total lifetime. .

7. The method for predicting the remaining life of an aero-engine by integrating machine learning and an improved GM(1,N) model according to claim 6, characterized in that: The specific process of determining the optimal total lifetime estimate from the candidate total lifetime set and directly outputting the remaining lifetime prediction at the current moment includes the following steps: In the total lifetime candidate set When searching, for each candidate total lifetime , in each time window The optimal parameter vector of the model obtained through the IRLS method The global fitting error is obtained by summing the corresponding relative and absolute errors. Then, the optimal total life estimate is determined by minimizing the global fitting error of multiple windows for the same engine. ; Based on the optimal total lifetime estimate and the running time or number of loops at the current moment. Calculate the predicted remaining lifetime at the current moment: .

8. The method for predicting the remaining life of an aero-engine by integrating machine learning and an improved GM(1,N) model according to claim 4, characterized in that: The total lifetime estimate and corresponding global fitting error output by the improved GM(1,N) model are used as gray features, fused with the standardized feature sequence, and then input into the machine learning model. The specific steps for further optimizing the prediction results through data-driven methods include: Construct a fusion feature vector, which includes the original feature sequence output from the data preprocessing stage, the optimal total lifetime estimate, and the corresponding global fitting error; The training set of complete engine life cycle data and the fused feature vector are used as input features of the machine learning model. The training set is randomly truncated multiple times to generate multiple partial life cycle input samples. Each partial life cycle input sample contains all the running data from the start of engine operation to the random truncation time. Each partial life cycle input sample is also set with a remaining life cycle label, which is the remaining running time from the truncation time to the engine failure time. Using the unit number as the grouping basis, the machine learning model is trained by grouped cross-validation to optimize the model parameters and evaluate the generalization ability of the model at different running stages, so as to obtain the trained machine learning model. The test set engine operation data is input into the trained machine learning model. The root mean square error (RMSE) and its standard deviation stability index are used as comprehensive evaluation criteria to select the optimal machine learning model. For each type of model, the top K sub-models with the best cross-validation performance are retained. During prediction, the ensemble prediction result is obtained by averaging the outputs of the top K sub-models. Finally, the remaining life prediction value of the fused machine learning model is obtained.

9. A device for predicting the remaining life of an aero-engine, characterized in that, include: The data preprocessing module, the adaptive window partitioning module, the grey modeling module for joint estimation of unknown total lifetime, the remaining lifetime search and optimization module, and the improved GM(1,N) model and machine learning fusion module are each used to execute the method steps of any one of claims 1 to 8, wherein: The data preprocessing module is used to generate standardized feature sequences by collecting multi-source operating data of aero-engines and performing cleaning, correlation analysis and standardization preprocessing. The adaptive window partitioning module is used to divide time series data into several time windows based on the stability criterion of data variation, so as to accurately and dynamically capture the degradation characteristics of the engine at different stages. The gray modeling module for joint estimation of unknown total lifetime is used to establish an improved GM(1,N) model for each window with unknown candidate total lifetime as the optimization variable, and solve the optimal parameter vector through the relative absolute error fitting criterion to realize the joint modeling of multiple variables on the remaining lifetime. The remaining lifetime search optimization module is used to dynamically adjust the search interval based on the total lifetime sample distribution in the training set, determine the optimal total lifetime estimate in the total lifetime candidate set, and directly output the remaining lifetime prediction value at the current moment, forming an independent gray prediction capability. An improved GM(1,N) model and machine learning fusion module is used to take the total lifetime estimate and corresponding global fitting error output by the improved GM(1,N) model as gray features, fuse them with the standardized feature sequence, and input them into the machine learning model. The prediction results are further optimized through data-driven methods to achieve synergy between the physical model and the data model.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method of any one of claims 1 to 8.

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