Method for predicting residual life of turbofan engine based on two-stage degradation label

Abstract

The invention relates to a turbofan engine residual life prediction method based on a two-stage degradation label. The method comprises the steps that sensor data of a turbofan engine are acquired and preprocessed; differentiated features are constructed based on physical attributes in the sensor data; adaptively determining the optimal segmentation number of the sensor data of each physical attribute by adopting piecewise linear fitting and an elbow method aiming at the sensor data, and obtaining a degradation turning point; a two-stage degradation label is constructed based on the degradation turning point, a TPRUL-Net prediction model fusing a BiLSTM network and an attention mechanism is constructed, and the TPRUL-Net prediction model is provided with a time sequence feature branch used for inputting differential features and the two-stage degradation label, a manual feature branch used for inputting statistical features obtained by sensor data, and a time sequence feature branch used for inputting the differential features and the two-stage degradation label. And the TPRUL-Net prediction model outputs a residual life prediction value according to a dual-branch fusion feature.

Description

Technical Field

[0001] This invention relates to the field of equipment failure prediction and health management, and in particular to a method for predicting the remaining life of a turbofan engine based on a two-stage degradation tag. Background Technology

[0002] In recent years, Prognostics and Health Management (PHM) has gained widespread attention in both academia and industry as a key research area for ensuring the safety and reliability of complex engineering systems. The core mission of PHM is to accurately predict the Remaining Useful Life (RUL) of equipment based on real-time monitoring data of equipment operating status and with the help of intelligent analysis methods. This provides a scientific and rational basis for preventative maintenance and condition-based repair, effectively avoiding losses and risks caused by sudden equipment failures.

[0003] In the aviation field, turbofan engines are the most critical core component of aircraft, and the performance degradation process of these engines has a direct and significant impact on flight safety and maintenance costs. A serious engine malfunction during flight can potentially lead to catastrophic consequences. Therefore, accurately predicting the RUL (Range Limiting) of engines during operation has become a core issue for improving aviation safety, reducing maintenance costs, and optimizing operational strategies.

[0004] In existing research literature, the RUL prediction methods for turbofan engines mainly cover the categories of mechanism-based modeling methods, data-driven methods, and hybrid methods.

[0005] Mechanism-based modeling methods primarily rely on a deep understanding of the engine's physical mechanisms, constructing degradation models of thermodynamic and aerodynamic coupling processes to predict engine lifespan. However, due to the extremely complex structure of turbofan engines and the highly nonlinear nature of their operating mechanisms, comprehensive and accurate modeling is difficult to achieve. This results in numerous limitations for these methods in practical engineering applications, often failing to accurately reflect the true degradation of the engine.

[0006] With the continuous advancement of sensor technology and the significant improvement in computing power, data-driven methods have gradually become the mainstream approach for predicting the RUL (Range Limit Uptime) of turbofan engines. These methods delve into the degradation patterns hidden within historical engine operating data and use statistical learning or deep learning models to predict the engine's future lifespan. In recent years, Recurrent Neural Networks (RNNs), Long Short-Term Memory Networks (LSTMs), Bidirectional LSTMs (BiLSTMs), Convolutional Neural Networks (CNNs), and their fusion structures have demonstrated outstanding performance in this field. For example, LSTMs can effectively alleviate the vanishing gradient problem and capture long-term dependencies in the data; BiLSTMs further enhance predictive capabilities by modeling forward and backward sequences; CNNs possess powerful feature extraction capabilities, and when combined with temporal models, they can achieve joint modeling of spatial-temporal degradation features. Simultaneously, attention mechanisms and multi-scale modeling methods have also been widely applied, highlighting key degradation stages and enhancing the model's sensitivity to features at different scales, thereby improving prediction accuracy.

[0007] To better align with the real-world characteristics of the multi-stage, nonlinear degradation of turbofan engines, researchers have begun focusing on staged prediction models, which have gradually become a significant research trend in recent years. These models typically use degradation point detection as a foundation, dividing the engine's lifecycle into multiple health stages and designing specialized prediction models for each stage. This aims to overcome the limitations of single models in adapting to the full-cycle degradation patterns of engines. For example, some studies employ a two-stage segmentation strategy, using change point detection to identify the health and degradation periods, and then applying CNN-LSTM and LSTM models respectively for modeling. Other studies utilize dual-task LSTM networks to simultaneously perform degradation stage classification and RUL regression, achieving fine-grained degradation modeling based on a seven-stage segmentation. Additionally, some studies have constructed a general "classification-regression" framework, dividing continuous sensor data into three states—"new / medium / heavy"—based on membership functions to adapt to the needs of different industrial scenarios. Overall, staged models, through a "stage segmentation—targeted modeling" strategy, effectively improve prediction accuracy under complex operating conditions.

[0008] However, the limitations of phased models are becoming increasingly apparent. On the one hand, phase division often relies on manually set parameters, lacking sufficient consideration of individual engine differences; on the other hand, if the division is too fine, it may lead to insufficient usability of the model in practical engineering applications. For example, the degradation process of engines from different batches and under different operating environments may differ, but manually set parameters are difficult to flexibly adapt to these changes.

[0009] Despite significant progress in predicting the RUL performance of turbofan engines, some problems remain to be solved.

[0010] Firstly, regarding feature construction, although some studies have introduced differential or statistical features, there is still a lack of differentiated feature extraction strategies for different types of sensor data. Various sensor data from engines have different characteristics and variation patterns, and general feature extraction methods cannot fully extract the effective information from the data, thus limiting the model's ability to represent complex degradation patterns.

[0011] Secondly, regarding label construction, most methods assume that all engines share a uniform maximum lifespan, meaning they all start with a fixed initial RUL value and enter the linear degradation phase. This approach is overly simplistic, ignoring the individual differences in the actual lifespan and degradation rate of engines, making it difficult to accurately describe the true nonlinear degradation process of engines. In reality, due to factors such as manufacturing processes, operating environments, and maintenance conditions, different engines exhibit significant differences in their degradation processes, and a uniform label construction method cannot accurately reflect these differences.

[0012] Third, while some studies have attempted to combine degradation point detection to generate adaptive maximum lifespan labels for different engines, they generally use a single linear function to describe the degradation of the engine throughout its entire lifespan. This approach is insufficient in capturing the nonlinear transition of the engine from its healthy phase to its accelerated degradation phase, and cannot accurately reflect the complex changes during the engine degradation process.

[0013] Fourth, existing degradation point detection methods typically rely on manually setting the number of segments or fixed parameters, resulting in poor adaptability and difficulty in stably and accurately identifying truly physically significant degradation inflection points. Different engines may have different degradation modes and inflection points, and detection methods with fixed parameters cannot flexibly address these differences, thus affecting the accuracy and reliability of staged prediction models.

[0014] It is evident that although some progress has been made in the field of turbofan engine RUL prediction, in order to further improve the accuracy and reliability of prediction, it is necessary to solve the problems in feature construction, label construction, degradation point detection, etc., so as to better meet the actual needs of the aviation industry for engine health management. Summary of the Invention

[0015] The technical problem to be solved by the present invention is to provide a method for predicting the remaining life of a turbofan engine based on a two-stage degradation label.

[0016] To achieve the above-mentioned objectives, this invention provides a method for predicting the remaining life of a turbofan engine based on a two-stage degradation tag, comprising the following steps: S1. Acquire sensor data from the turbofan engine and perform preprocessing; S2. Construct differentiated features based on physical attributes in sensor data; S3. For sensor data, the optimal number of segments for each physical attribute sensor data is adaptively determined by combining piecewise linear fitting and elbow method, and the degradation inflection point of the turbofan engine as a whole is obtained by multi-sensor breakpoint fusion algorithm. S4. Construct a two-stage degradation label based on the degradation inflection point, wherein a stable degradation label is constructed before the degradation inflection point, and a nonlinear accelerated degradation label is constructed after the degradation inflection point. S5. Construct a TPRUL-Net prediction model that integrates a BiLSTM network and an attention mechanism. The TPRUL-Net prediction model is configured with a temporal feature branch for inputting differential features and two-stage degradation labels, and a handcrafted feature branch for inputting statistical features obtained from sensor data. The TPRUL-Net prediction model outputs the remaining lifetime prediction value with the fused features of the two branches. S6. Acquire sensor data of the turbofan engine under test, and use the TPRUL-Net prediction model to predict the remaining service life of the turbofan engine under test.

[0017] According to one aspect of the present invention, in step S1, the step of acquiring and preprocessing the sensor data of the turbofan engine, the sensor data is time-series data, and the preprocessing includes: outlier removal and normalization processing.

[0018] According to one aspect of the present invention, in step S2, in the step of constructing differentiated features based on physical attributes in sensor data, for sensor data with physical attributes of pressure and flow rate, proportional operation is used to construct consistent change features that evolve over time, and for sensor data with physical attributes of temperature and vibration, difference operation is used to construct abnormal features that accumulate over time, and the sensor data is enhanced based on the consistent change features and abnormal features to construct differentiated features.

[0019] According to one aspect of the present invention, in step S2, in the step of constructing differentiated features based on physical properties in sensor data, the sensor data of the first working cycle of the turbofan engine is used as the reference sensor data, and the sensor data of subsequent working cycles are proportionally calculated or differentially calculated with the reference sensor data to construct corresponding features.

[0020] According to one aspect of the present invention, step S3, which involves adaptively determining the optimal number of segments for each physical attribute of the sensor data by combining piecewise linear fitting and the elbow method, and obtaining the overall degradation inflection point of the turbofan engine through a multi-sensor breakpoint fusion algorithm, includes: Principal component analysis was performed on the preprocessed sensor data, and a preset number of principal components were retained as PCA dimensionality reduction data. Low-pass filtering is applied to the PCA dimensionality reduction data to eliminate noise interference; Piecewise linear fitting is performed on the PCA dimensionality reduction data of the sensor after low-pass filtering. After completing piecewise linear fitting for different orders, the second-order residual sum of squares is calculated. Finally, the position corresponding to the minimum value of the second-order difference is found as the elbow turning point, and the optimal number of segments for the sensor data of each physical attribute is determined. The multi-sensor breakpoint fusion algorithm based on slope mutation calibration is used to filter the piecewise linear fitting results under the optimal number of segments to obtain the overall degradation inflection point of the turbofan engine.

[0021] According to one aspect of the present invention, the step of obtaining the overall degradation inflection point of a turbofan engine by filtering the piecewise linear fitting results under the optimal number of segments using a multi-sensor breakpoint fusion algorithm based on slope abrupt calibration includes: Based on the piecewise linear fitting results, the fitting breakpoints of each segment are obtained, and the effective breakpoints among the fitting breakpoints are selected. Cluster feature vectors are constructed based on the correlation coefficient. The correlation coefficient is obtained by calculating the absolute value of the Pearson correlation coefficient between the values ​​of the first and last two moments of the sensor data and the corresponding running cycle. K-means clustering was used to group similar valid breakpoints into several groups. After removing extreme values ​​from each group of valid breakpoints using the 3σ criterion, the groups were weighted and fused within each group using the correlation coefficient as the weight. For each effective breakpoint group after intra-group weighted fusion, the inter-group weights are calculated based on the average relevance and breakpoint consistency to complete the cross-group weighted fusion. If the number of effective breakpoints is less than the number of clusters, the fusion breakpoint is obtained directly by relevance weighted average as the degradation inflection point.

[0022] According to one aspect of the present invention, in step S4, the step of constructing a two-stage degradation label based on the degradation inflection point, wherein the stable degradation label is constructed based on a linear decay model, and the nonlinear accelerated degradation label is constructed by introducing an accelerated decay factor, then the constructed two-stage degradation label can be expressed as:

[0023] in, Indicates a degradation label. This represents the total number of cycles of the turbofan engine within the observation period. This indicates the current cycle number of the turbofan engine. This indicates the turning point in the overall degradation of a turbofan engine. This indicates the rate of acceleration attenuation.

[0024] According to one aspect of the invention, the acceleration decay factor introduced by the nonlinear accelerated degradation label is obtained based on the following steps: The first average degradation slope of the turbofan engine is obtained by acquiring sensor data before the degradation inflection point. The second average degradation slope of the turbofan engine's nonlinear accelerated degradation is obtained from sensor data after the degradation inflection point. The degradation slope ratio of each sensor in the turbofan engine is obtained based on the second average degradation slope and the first average degradation slope. The average slope ratio of the turbofan engine is obtained based on the degradation slope ratio of each sensor, and the effective slope ratio range of the turbofan engine is obtained by expanding the average slope ratio. Based on the effective rate range of all turbofan engines, the interval is summarized to obtain the overall engine acceleration decay rate reference interval, and the value of the acceleration decay rate to be introduced is obtained by taking the value of the acceleration decay rate reference interval.

[0025] According to one aspect of the present invention, in step S5, the step of constructing a TPRUL-Net prediction model that integrates a BiLSTM network and an attention mechanism, wherein the TPRUL-Net prediction model includes: a temporal feature branch, a handmade feature branch, a feature concatenation layer, and an output layer; The temporal feature branch includes: a first input layer, a BiLSTM network, an attention mechanism module, and a first linear layer; The first input layer is used to receive differential features and two-stage degradation labels and process them with a sliding time window to output a first feature tensor sequence with a fixed step size; The BiLSTM network captures degradation information based on forward and backward dependencies based on the first feature tensor sequence; The attention mechanism module generates attention weights in the time dimension based on the degradation information, highlights the feature contribution of degradation information at key moments, and uses residual connections to fuse the attention weights with the degradation information to generate temporal features. The first linear layer receives the temporal features and outputs them after flattening. The handcrafted feature branch includes: a second input layer, a statistical module, a Z-Score normalization layer, and a second linear layer; The second input layer is used to receive sensor data and process it with a sliding time window to output a second feature tensor sequence with a fixed step size; The statistical module extracts statistical features based on the second feature tensor sequence, wherein the statistical features include: mean, standard deviation, and degradation trend coefficient; The Z-Score normalization layer is used to receive statistical features and perform Z-Score standardization. The second linear layer receives the statistical features after Z-Score standardization and flattens them before outputting the result; The feature splicing layer receives temporal features output from the temporal feature branch and statistical features output from the manual feature branch, and splices them along the feature dimension to obtain a dual-branch fused feature; The output layer maps a single non-negative real number based on fused features, which serves as a prediction of the remaining lifespan of the turbofan engine.

[0026] According to one aspect of the invention, the optimal number of segments is 5.

[0027] According to one aspect of the present invention, this approach generally outperforms traditional methods in terms of prediction accuracy and robustness, and is of great significance for enhancing the application value of PHM for turbofan engines.

[0028] According to one aspect of the present invention, after verification on the FD001 subset of C-MAPSS, it can be seen that the present invention has significant advantages over traditional methods, and can effectively capture the real degradation law of turbofan engines, providing a reliable technical path for PHM of turbofan engines.

[0029] According to one aspect of the present invention, the TPRUL-Net prediction model captures temporal dependencies through bidirectional LSTM, emphasizes the contribution of key moment features by combining an attention mechanism, and introduces statistical feature branches to achieve cross-stage auxiliary representation, thereby enhancing prediction accuracy and robustness.

[0030] According to one aspect of the present invention, this solution, based on the combination of two-stage degradation labels and the TPRUL-Net prediction model, not only possesses advantages in predictive performance but also provides an interpretable and scalable solution for degradation process modeling and stage-specific prediction in the field of PHM (Prognostics and Health Management). This allows the solution to be extended to multi-condition and multi-failure-mode scenarios in the future and has the potential to be embedded in digital twins and intelligent maintenance systems, thereby realizing application value in safety-critical fields such as aviation, energy, and manufacturing.

[0031] According to one aspect of the present invention, this approach provides a new modeling perspective for predicting the remaining life (RUL) of turbofan engines. By introducing the acceleration phase degradation factor α during the labeling process and determining its reasonable range based on the slope variation distribution at the degradation inflection points of multiple engines, the proposed method overcomes the limitation of traditional static RUL labeling in failing to reflect nonlinear degradation laws, making the prediction problem modeling more closely aligned with actual physical processes. Attached Figure Description

[0032] Figure 1This is a flowchart illustrating the steps of the turbofan engine remaining life prediction method based on two-stage degradation tags of the present invention. Figure 2 This is a flowchart of the turbofan engine remaining life prediction method based on two-stage degradation tags according to the present invention. Figure 3 This is a flowchart illustrating the process of obtaining the degradation inflection point in this invention. Figure 4 This is a structural diagram of the LSTM model of the present invention; Figure 5 This is a structural diagram of the BiLSTM model of the present invention; Figure 6 This is a structural diagram of the TPRUL-Net prediction model of the present invention; Figure 7 This is a comparison of the original sequence of sensor data from the present invention with the fitting strategy in a fixed two-stage phase and the optimal breakpoint position obtained by the present solution. Figure 8 This is a comparison of the original sequence of sensor data from the present invention with the optimal breakpoint position obtained by the fixed 3-stage fitting strategy and the present solution. Figure 9 This is a comparison of the original sequence of sensor data from the present invention with the optimal breakpoint position obtained by the fixed 4-stage fitting strategy and the present solution. Figure 10 This is a comparison of the original sequence of sensor data from the present invention with the optimal breakpoint position obtained by the fixed 5-stage fitting strategy and the present solution. Figure 11 This is a data diagram of the sliding time window processing of the present invention; Figure 12 This is a two-stage degradation label diagram of the present invention; Figure 13 This is a graph showing the RUL prediction results of engine 3 in the FD001 dataset of the present invention; Figure 14 This is a graph showing the RUL prediction results of engine 27 in the FD001 dataset of the present invention; Figure 15 This is a graph showing the RUL prediction results of engine 93 in the FD001 dataset of the present invention. Detailed Implementation

[0033] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The embodiments cannot be described in detail here, but the embodiments of the present invention are not limited to the following embodiments.

[0034] Combination Figure 1 and Figure 2As shown, according to one embodiment of the present invention, a method for predicting the remaining life of a turbofan engine based on a two-stage degradation tag includes the following steps: S1. Acquire sensor data from the turbofan engine and perform preprocessing; S2. Construct differentiated features based on physical attributes in sensor data; S3. Piecewise linear fitting and elbow method are used to adaptively determine the optimal number of segments for each physical property of the sensor data, and the degradation inflection point of the turbofan engine as a whole is obtained through multi-sensor breakpoint fusion algorithm. S4. Construct two-stage degradation labels based on degradation inflection points, wherein a stationary degradation label is constructed before the degradation inflection point, and a nonlinear accelerated degradation label is constructed after the degradation inflection point. S5. Construct a TPRUL-Net prediction model that integrates BiLSTM network and attention mechanism. The TPRUL-Net prediction model has a temporal feature branch for inputting differential features and two-stage degradation labels, and a handmade feature branch for inputting statistical features obtained from sensor data. The TPRUL-Net prediction model outputs the remaining lifetime prediction value with the fused features of the two branches. S6. Acquire sensor data of the turbofan engine under test, and use the TPRUL-Net prediction model to predict the remaining service life of the turbofan engine under test.

[0035] According to one embodiment of the present invention, in step S1, the sensor data of the turbofan engine is acquired and preprocessed. The sensor data is time-series data, and the preprocessing includes outlier removal and normalization. In this embodiment, during the preprocessing of the sensor data, it can be further organized in a fixed format to establish a clean and stable input foundation for subsequent feature construction and modeling.

[0036] According to one embodiment of the present invention, in step S2, the step of constructing differentiated features based on the physical attributes in the sensor data, the sensor data can be collected based on different types of sensors, specifically: pressure sensors, flow sensors, temperature sensors, and vibration sensors; therefore, the sensor data as a whole is composed of data with different physical attributes. Thus, for sensor data with physical attributes of pressure and flow, proportional calculation is used to construct consistent change features that evolve over time, and for sensor data with physical attributes of temperature and vibration, difference calculation is used to construct abnormal features that accumulate over time. Based on the consistent change features and abnormal features, the sensor data is enhanced to construct differentiated features.

[0037] In this embodiment, in order to better and more accurately capture the engine degradation patterns of different turbofan engines, the sensor data of the first working cycle of the turbofan engine is used as the reference sensor data. Then, the sensor data of each subsequent working cycle is proportionally or differentially calculated with the reference sensor data to construct the corresponding features, thereby obtaining the relative change over time.

[0038] Through the above settings, this scheme effectively eliminates the initial differences between different engines, highlights the relative deviations in the degradation process, and enhances the scheme's sensitivity to performance degradation trends. Simultaneously, by combining the physical properties of the sensors, a proportional approach is used for pressure and flow parameters to reflect consistent changes across different dimensions; for temperature and vibration parameters, a difference approach is used to highlight anomalies accumulated over time. Therefore, based on this targeted feature construction method, the model of this scheme can not only learn more physically meaningful degradation characteristics but also improve the comparability and predictive effectiveness between different engines.

[0039] In this embodiment, the step of constructing differentiated features based on physical properties in sensor data includes: Acquiring sensor data ,in, , ,..., This represents the sensor vector formed during a single work cycle. Construct a sensor type mapping function to classify pressure, flow, temperature, and vibration data based on the sensor type mapping function; The sensor data (i.e., sensor vectors) from the first work cycle (This refers to) reference sensor data; Traverse the current sensor vector Each sensor in If the sensor's physical properties are pressure or flow rate, then the formula for calculating the consistent change characteristics over time using proportional calculations is as follows:

[0040] in, Indicates consistent change characteristics. Represents the current sensor vector Each sensor in Data (only data related to stress or traffic is extracted here). Represents reference sensor data (i.e., sensor vectors) Each sensor in ) Data (only data related to pressure or traffic is extracted here).

[0041] If the sensor's physical properties are temperature-related and vibration-related, then the formula for calculating the accumulated abnormal characteristics over time using difference calculation is as follows:

[0042] in, Indicates abnormal characteristics, Represents the current sensor vector Each sensor in Data (only temperature and vibration data are extracted here). Represents reference sensor data (i.e., sensor vectors) Each sensor in ) Data (only temperature and vibration data are extracted here).

[0043] The resulting consistent variation features and anomalous features are merged with the original sensor data to obtain the final differentiated features, thereby enhancing the sensor data. The merged differentiated features are represented as follows:

[0044] in, This represents the enhanced sensor data, i.e., the differentiated features. This represents a data sequence constructed from anomalous features. This represents a data sequence constructed from consistent variation characteristics.

[0045] like Figure 3 As shown, according to one embodiment of the present invention, step S3, which involves adaptively determining the optimal number of segments for each physical attribute of the sensor data by combining piecewise linear fitting and the elbow method, and obtaining the overall degradation inflection point of the turbofan engine through a multi-sensor breakpoint fusion algorithm, includes: Principal component analysis was performed on the preprocessed sensor data, and a preset number of principal components were retained as PCA dimensionality reduction data. Low-pass filtering is applied to the PCA dimensionality reduction data to eliminate noise interference; Piecewise linear fitting is performed on the PCA-reduced sensor data after low-pass filtering. After piecewise linear fitting at different orders, the second-order residual sum of squares (RSS) is calculated. The position corresponding to the minimum value of the second-order difference is finally found as the elbow inflection point, and the optimal number of segments for each physical attribute of the sensor data is determined. The residual sum of squares (RSS) decreases continuously with the increase in the number of segments, but the rate of decrease gradually slows down. Then, the first-order difference of the RSS sequence is calculated to reflect its decreasing rate, and a second-order difference is performed on the first-order difference to characterize the rate of change of the decreasing rate. Finally, the position corresponding to the minimum value of the second-order difference is found, which is the elbow inflection point where the decreasing rate of the residual sum of squares (RSS) slows down. In this embodiment, the optimal number of segments can be set to 5. Specifically, since the improvement in the training results of the prediction model is not significant when the number of fitted segments exceeds 5, the maximum number of segments based on adaptive fitting is limited to 5 to ensure that this scheme achieves an optimal match between fitting computational load and prediction accuracy.

[0046] The multi-sensor breakpoint fusion algorithm based on slope mutation calibration is used to filter the piecewise linear fitting results under the optimal number of segments to obtain the overall degradation inflection point of the turbofan engine.

[0047] like Figure 3 As shown, according to one embodiment of the present invention, the step of filtering the piecewise linear fitting results under the optimal number of segments to obtain the overall degradation inflection point of the turbofan engine using a multi-sensor breakpoint fusion algorithm based on slope mutation calibration includes: Based on the piecewise linear fitting results, the fitting breakpoints for each segment are obtained, and the effective breakpoints are selected. Furthermore, a clustering feature vector is constructed based on the correlation coefficient. The correlation coefficient is obtained by calculating the absolute value of the Pearson correlation coefficient between the values ​​of the sensor data at the first and last two moments and the corresponding operating cycle. Specifically, firstly, the sensor data sequence and the corresponding periodic sequence within the complete operating cycle are obtained. For example, the periodic sequence is represented as: `cycle_full = np.array([1,2,3,4,5,6,7,8,9,10])` represents a complete running cycle. The sensor data sequence is represented as follows: Y = np.array([2.1,4.0,6.2,8.1,10.3,12.2,14.1,16.0,18.2,20.1]), represents the corresponding values ​​of the sensor in one complete operating cycle; Secondly, the first and last two elements of the cycle sequence are extracted to form an array of independent variables, and the first and last two elements of the sensor data sequence are extracted to form an array of dependent variables. For example, the array of independent variables is: α = [cycle_full[0], cycle_full[-1]], and the extracted data is [1, 10]; the array of dependent variables is: β = [Y[0], Y[-1]], and the extracted data is [2.1, 20.1].

[0048] Next, calculate the Pearson correlation coefficient for the array of independent variables and the array of dependent variables. The formula is: corr_coef,p_value=pearsonr(α,β). Therefore, the p_value can be ignored, and the absolute value of the correlation coefficient, abs(corr_coef), is output as the correlation coefficient.

[0049] K-means clustering was used to group similar valid breakpoints into several groups. After removing extreme values ​​from each group of valid breakpoints using the 3σ criterion, the groups were weighted and fused within each group using the correlation coefficient as the weight. For each effective breakpoint group after weighted fusion within the group, the inter-group weights are calculated based on the average correlation and breakpoint consistency (which can be the inverse of the standard deviation), thus completing the cross-group weighted fusion. If the number of effective breakpoints is less than the number of clusters, the fusion breakpoint is obtained directly by using the correlation weighted average as the degradation inflection point. In this embodiment, the arithmetic mean of the absolute values ​​of the correlation coefficients (i.e., the absolute values ​​of the Pearson correlation coefficients of each PCA component's "first and last values ​​- running period") corresponding to all PCA components (i.e., PCA dimensionality reduction data) within a breakpoint group is calculated.

[0050] Through the above settings, this solution achieves precise positioning of degradation points through three-stage collaboration, enabling more accurate labeling of subsequent two-stage degradation tags. This allows the solution to generate RUL tags that better reflect actual degradation characteristics, greatly improving the applicability and prediction accuracy of the solution.

[0051] According to one embodiment of the present invention, in step S4, the step of constructing a two-stage degradation label based on the degradation inflection point, wherein the stable degradation label is constructed based on a linear decay model, and the nonlinear accelerated degradation label is constructed by introducing an accelerated decay factor, then the constructed two-stage degradation label can be expressed as:

[0052] in, Indicates a degradation label. This represents the total number of cycles of the turbofan engine within the observation period. This indicates the current cycle number of the turbofan engine. This indicates the turning point in the overall degradation of a turbofan engine. This indicates the rate of acceleration attenuation.

[0053] Through the above settings, based on the obtained degradation inflection points, the characteristics of different starting points for sensor data recording in turbofan engines can be fully adapted (e.g., some are recorded from scratch, and some are recorded only near the degradation stage). Furthermore, based on the construction of two-stage degradation labels, the nonlinear process of "small linear degradation during stable operation → significant accelerated degradation in the early stage of failure" can be accurately captured. Moreover, since the corresponding degradation inflection points can be accurately obtained, abrupt changes in labels at the degradation inflection points can be effectively avoided, making the prediction accuracy of this scheme more beneficial. It fully eliminates the learning and prediction bias of the model caused by abrupt changes in labels, and is more in line with the physical law of the smooth transition from "stable to accelerated" in the degradation process of turbofan engines.

[0054] like Figure 1 As shown, according to one embodiment of the present invention, the accelerated decay factor introduced by the nonlinear accelerated degradation label is obtained based on the following steps: The first average degradation slope of the turbofan engine is obtained by acquiring sensor data before the degradation inflection point. The second average degradation slope of the turbofan engine's nonlinear accelerated degradation is obtained from sensor data after the degradation inflection point. The degradation slope ratio of each sensor in the turbofan engine is obtained based on the second average degradation slope and the first average degradation slope. The average slope ratio of the turbofan engine is obtained based on the degradation slope ratio of each sensor, and the effective slope ratio range of the turbofan engine is obtained by expanding the average slope ratio. Based on the effective rate range of all turbofan engines, the interval is summarized to obtain the overall engine acceleration decay rate reference interval, and the value of the acceleration decay rate to be introduced is obtained by taking the value of the acceleration decay rate reference interval.

[0055] Combination Figure 4 , Figure 5 and Figure 6As shown, according to one embodiment of the present invention, in step S5, the step of constructing the TPRUL-Net prediction model integrating a BiLSTM network and an attention mechanism, the TPRUL-Net prediction model includes: a temporal feature branch, a handcrafted feature branch, a feature concatenation layer, and an output layer; in this embodiment, the temporal feature branch includes: a first input layer, a BiLSTM network, an attention mechanism module, and a first linear layer; wherein, the first input layer is used to receive differential features and two-stage degradation labels and process them with a sliding time window to output a first feature tensor sequence with a fixed step size; in this embodiment, the sliding time window can make full use of time information to promote the accuracy and reliability of RUL prediction results; specifically, the window size of the sliding time window is set to 30, so as not to exceed the shortest cycle length of the turbofan engine cycle in the sensor data. The time window is designed to be overlapping, and the step size is set to 1.

[0056] In this embodiment, the BiLSTM network captures degradation information based on forward and backward dependencies using a first feature tensor sequence. The BiLSTM network consists of two LSTM models; during training, one LSTM model is trained as a forward layer, and the other as a backward layer to process the input features. This allows it to capture both past and future information and utilize it during testing. Therefore, this bidirectional structure enables a more comprehensive understanding of the sequence context, making it particularly suitable for tasks requiring complete sequence context, and significantly improving the predictive power and accuracy of the proposed solution.

[0057] In this implementation, an LSTM model typically includes three gates: a forget gate, an input gate, and an output gate. The forget gate controls the information to be forgotten during model training, the input gate updates the existing model parameters based on the input data, and the output gate controls the output based on the input and current state information. The forget gate determines whether to retain or delete information, a decision based on the weighted assignment of input features. During LSTM model training, the forget gate is calculated using the sigmoid function, and its decision is based on the cell state at the previous time step. and current input Output of the forget gate The value ranges from 0 to 1: where 0 represents completely discarding the feature information, and 1 represents retaining all the information of the feature. Its mathematical expression can be written as:

[0058] in, It is the sigmoid activation function. It is a bias term. It is a weight matrix.

[0059] The input gate determines whether to add new information to the LSTM's memory. It consists of two layers: a sigmoid layer and a tanh layer. The sigmoid layer decides whether to include information, while the tanh layer updates the memory by adding information relevant to important features. Finally, the outputs of these two layers are combined to update the values ​​in the LSTM's memory, as shown in the following formula:

[0060]

[0061] in, The output of the sigmoid layer represents the weights for selecting and discarding candidate information at time t. This represents the weight matrix of the input gate sigmoid layer. This represents the bias term of the input gate sigmoid layer. This represents the output of the tanh layer. This represents the weight matrix of the input gate tanh layer.

[0062] The output gate determines which information to output from the LSTM unit. Based on the current input and cell state, it filters out information relevant to the current task and outputs it. Its computation involves two steps: first, an output mask is generated through a sigmoid layer. The formula for determining which parts of the cell state will be output is as follows:

[0063] in, The value range is between 0 and 1, where 1 means to output the corresponding information completely and 0 means to completely suppress the information. For bias terms, This represents the cell state at the previous moment. For the current input, This represents the weight matrix of the output gate sigmoid layer.

[0064] Secondly, the cell state ( The value is processed using the tanh function (compressing it to between -1 and 1), and then compared with the output mask. Multiply by , and get the final output value ( The calculation formula is:

[0065] in, This represents the cell state after the LSTM update at time t. It serves as both the output of the current moment and the hidden state of the next moment in the calculation, thus enabling the sequential transmission of information.

[0066] In this embodiment, the AttentionMouble module generates attention weights in the time dimension based on degradation information, highlighting the feature contribution of degradation information at key moments, and uses residual connections to fuse the attention weights with degradation information to generate temporal features. In this embodiment, the AttentionMouble module specifically generates attention weights in the time dimension through the set fully connected layer and softmax activation function, which will not be elaborated here.

[0067] In this embodiment, the first linear layer receives the temporal features, flattens them, and outputs them as a low-dimensional compact representation.

[0068] In this embodiment, the manual feature branch includes: a second input layer, a statistical module, a Z-Score normalization layer, and a second linear layer. The second input layer receives sensor data and processes it using a sliding time window to output a second feature tensor sequence with a fixed step size. In this embodiment, the sliding time window fully utilizes temporal information to improve the accuracy and reliability of RUL prediction results. Specifically, the window size of the sliding time window is set to 30, so as not to exceed the shortest cycle length of the turbofan engine cycle in the sensor data. The time window is designed to overlap, with a step size of 1.

[0069] In this embodiment, the statistical module extracts statistical features based on the second feature tensor sequence, wherein the statistical features include: mean, standard deviation and degradation trend coefficient; in this embodiment, the degradation trend coefficient is specifically represented by slope.

[0070] In this embodiment, the Z-Score normalization layer is used to receive statistical features and perform Z-Score standardization.

[0071] In this embodiment, the second linear layer receives the statistical features after Z-Score standardization, flattens them, and outputs the mapped feature representation.

[0072] In this embodiment, the feature splicing layer receives the temporal features output by the temporal feature branch and the statistical features output by the manual feature branch, and splices them along the feature dimension to obtain the fused features of the two branches.

[0073] In this embodiment, the output layer maps a single non-negative real number based on the fused feature map as a prediction of the remaining lifespan of the turbofan engine.

[0074] According to one embodiment of the present invention, in step S6, sensor data of the turbofan engine under test is acquired, and the remaining service life of the turbofan engine under test is predicted using the TPRUL-Net prediction model. The TPRUL-Net prediction model is pre-trained based on the aforementioned settings, and after training, it can predict the remaining service life of the turbofan engine under test based on the sensor data. In this embodiment, the TPRUL-Net prediction model uses the Adam optimizer (learning rate 0.0002) during pre-training, employs LeakyReLU (slope 0.01) in the hidden layers, and sets a dropout of 0.4 in the fully connected layers to alleviate overfitting.

[0075] In this embodiment, during the training of the TPRUL-Net prediction model, a scoring function and the RMSE index can be used to evaluate its prediction results until the evaluation of its prediction results meets the corresponding preset threshold, thus completing the training iteration.

[0076] In this embodiment, the scoring function is an indicator proposed by the International Conference on Predictive and Health Management (PHM08) Data Challenge to quantify the predictive power of the model, and it is expressed as:

[0077] in, It is the number of test samples. It is the difference between the actual value and the predicted value. The scoring function is asymmetric, imposing a greater penalty on later predictions compared to earlier predictions.

[0078] In this implementation, the RMSE index is a standard forecasting evaluation metric that imposes equal penalties on early and late forecasts. Its calculation formula is as follows:

[0079] Among them, the lower the values ​​of the scoring function and RMSE index, the better the prediction result.

[0080] According to one embodiment of the present invention, the turbofan engine remaining life prediction method based on two-stage degradation tags can be implemented based on a turbofan engine remaining life prediction device based on two-stage degradation tags, wherein the turbofan engine remaining life prediction device includes: The preprocessing module is used to acquire and preprocess sensor data from the turbofan engine. The differential feature construction module is used to construct differential features based on the physical properties in sensor data; The degradation inflection point determination module is used to adaptively determine the optimal number of segments for each physical property of the sensor data by piecewise linear fitting and elbow method, and obtain the overall degradation inflection point of the turbofan engine through a multi-sensor breakpoint fusion algorithm. The two-stage degradation label construction module is used to construct two-stage degradation labels based on degradation inflection points. Specifically, a stationary degradation label is constructed before the degradation inflection point, and a nonlinear accelerated degradation label is constructed after the degradation inflection point. The TPRUL-Net prediction model building module is used to build a TPRUL-Net prediction model that integrates BiLSTM network and attention mechanism. The TPRUL-Net prediction model is set with a temporal feature branch for inputting differential features and two-stage degradation labels, and a handmade feature branch for inputting statistical features obtained from sensor data. The TPRUL-Net prediction model outputs the remaining lifetime prediction value with the fused features of the two branches. The prediction module is used to load the trained TPRUL-Net prediction model and acquire sensor data of the turbofan engine under test, and to predict the remaining service life of the turbofan engine under test using the TPRUL-Net prediction model.

[0081] Specific limitations regarding the turbofan engine remaining life prediction device based on two-stage degradation tags can be found in the limitations of the turbofan engine remaining life prediction method based on two-stage degradation tags mentioned above, and will not be repeated here. Each module in the aforementioned turbofan engine remaining life prediction device based on two-stage degradation tags can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each module.

[0082] In this embodiment, the memory may be, but is not limited to, Random Access Memory (RAM), Read Only Memory (ROM), Programmable Read-Only Memory (PROM), Erasable Programmable Read-Only Memory (EPROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), etc.

[0083] In this embodiment, the processor can be an integrated circuit chip with signal processing capabilities. The processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0084] To further illustrate this plan, further examples will be provided.

[0085] a. Introduction to the dataset In this embodiment, the C-MAPSS dataset is used; specifically, the C-MAPSS dataset is divided into four sub-datasets, labeled FD001, FD002, FD003, and FD004, respectively. The datasets differ in the number of engines used for training and testing, operating conditions, failure modes, and sample size. Detailed information about the C-MAPSS dataset is shown in Table 1.

[0086] Table 1

[0087] Taking the FD001 dataset as an example, the training set contains 3 operating parameters and 21 sensor data points, providing multivariate time series data. The training dataset collects sensor records of operational failures from multiple aero-engine units under various operating settings and failure modes. The initial wear of each engine unit differs, and manufacturing variations are unknown, thus considered normal. The engine units gradually degrade until system failure occurs. The sensor records in the test dataset cease at a point in time before the system failure occurs.

[0088] The specific information for the 21 sensors in the dataset can be found in Table 2.

[0089] Table 2

[0090] b. Sensor data preprocessing After analyzing the data in subset FD001, we found that the sensor data in columns 5, 9, 10, 14, 20, 22, and 23 of the original dataset remained constant and did not significantly help with model training. Therefore, in the data preprocessing step, we first removed useless sensor features, then constructed difference features from the sensor data according to the aforementioned steps (i.e., the steps of constructing differential features based on the physical properties in the sensor data) and added them to the original training data. Finally, we performed max-min normalization on the degradation data of different engines along the column direction; the max-min formula is shown below:

[0091] in, Let represent the normalized value of the j-th feature at the i-th data point. This represents the original values ​​of the data before normalization. Let represent the minimum value of the j-th feature. This represents the maximum value of the j-th feature.

[0092] c. Obtaining the degeneration inflection point To obtain fitting breakpoints that better reflect the original data, this study employs a combination of piecewise linear fitting (PwLF) and the elbow method to adaptively determine the number of fitting segments for different sensor data, with a total of 5 fitting segments. Specifically, Figure 7 , Figure 8 , Figure 9 and Figure 10 This paper presents the original sequence of sensor data and the piecewise linear fitting results under different fitting strategies. The blue solid line represents the filtered original data, the red curve is the broken line connecting the fitting breakpoints, the red dashed lines mark the breakpoints obtained using different orders of fitting, and the green dashed lines mark the optimal breakpoint position determined by the elbow method improved in this scheme for piecewise linear fitting. Analysis shows that fixed-segment fitting is easily affected by local fluctuations, causing the first breakpoint of the fitted curve to appear earlier or later in some intervals. In contrast, the adaptive fitting curve better matches the trend of the original data, making the location of significant change points (red vertical lines) more accurate and robust, thus providing a reliable basis for the subsequent construction of two-stage degradation labels.

[0093] d. Constructing two-stage degradation labels In this embodiment, a two-stage degradation label is constructed for the degradation process of the turbofan engine based on the aforementioned degradation inflection point. The specific method is as described above and will not be repeated here.

[0094] e. Sliding time window processing See Figure 11Based on the aforementioned settings for the sliding time window, 17,731 training samples were obtained using a given window length (i.e., tw, TimeWindow) and step size. During the testing and training phases, the remaining lifespan of each turbofan engine was predicted using the last sensor measurement data from the final time window.

[0095] f. Parameter settings for the TPRUL-Net prediction model In this implementation, the LSTM layer adopts a single-layer bidirectional structure, with 50 hidden units in each direction to capture degenerate features in the sequence. An attention mechanism is then introduced to highlight the contribution of key moments, and residual connections enhance feature stability. During the feature extraction stage, the network employs a dual-branch structure: on one hand, the attention-weighted temporal features are processed through two fully connected layers for dimensionality reduction and deep feature extraction; on the other hand, the mean, standard deviation, and slope of the input sequence are calculated and mapped to low-dimensional compact statistical features. The two branches are concatenated and connected to a single-neuron output layer, using ReLU activation to predict the remaining lifetime (RUL). During training, the Adam optimizer (learning rate 0.0002) is used, LeakyReLU (slope 0.01) is used in the hidden layers, and a dropout of 0.4 is set in the fully connected layers to alleviate overfitting. Furthermore, the parameters of the TPRUL-Net prediction model are summarized in Table 3.

[0096] Table 3

[0097] g. Test results To verify the effectiveness of this approach, comparative experiments were conducted. All experiments were based on the FD001 subset of the C-MAPSS dataset, using the RSME index and the Score function as evaluation metrics to ensure that the comparison results objectively reflect the impact of labeling methods on prediction performance.

[0098] Validation of feature construction To verify the rationality and effectiveness of the proposed differential features, the original features and the data after adding consistency variation features and outlier features were respectively input into the prediction model TPRUL-Net, and their prediction accuracy was compared under the same experimental conditions. The evaluation metrics used were the Score function and the RMSE index, and the results are shown in Table 4.

[0099] Table 4

[0100] The results in the table show that the model's prediction accuracy was significantly improved after introducing the new features. Specifically, the score decreased from 5261.17 to 366.72, and the RMSE decreased from 31.0481 to 16.9414, both better than the performance without the new features. This indicates that the newly constructed features can effectively express the engine degradation trend and improve the model's accuracy and robustness in predicting remaining life.

[0101] h. Constructing hyperparameters for two-stage degradation labels In this embodiment, the effective magnification range can be set to an average slope magnification extension of ±20%. Furthermore, a subset of FD001 is selected for training and testing. (The remaining text appears to be incomplete and requires further context.) The values ​​were tested. For each set of parameters, the training set labels were regenerated, and the TPRUL-Net prediction model was trained and validated. Finally, the prediction performance was evaluated using the Score function and RMSE metric. The experimental results are shown in Table 5.

[0102] Table 5

[0103] The experimental results show that when When the value is 1.5, the model achieves the best performance in both RMSE and Score metrics, effectively balancing the physical plausibility of the degradation trend with prediction accuracy. Therefore, this paper ultimately selects... =1.5 is used as the default parameter for two-stage tag construction.

[0104] After confirming hyperparameters After obtaining the value, the second-stage degradation label of the FD001 training set can be obtained, and as follows: Figure 12 As shown.

[0105] i. Validation of the effectiveness of two-stage degradation labeling To verify the effectiveness of the two-stage degradation labeling method, it was compared with the linear degradation labeling method commonly used in existing studies. The comparative experiment included three different label construction methods: the first method is uniform maximum life linear labeling, which sets the same maximum life for all engines and generates RUL labels in a linearly decreasing manner; the second method is individualized maximum life linear labeling, which sets the maximum life for each engine according to its actual degradation cycle and generates corresponding linear labels; the third method is the two-stage degradation labeling method proposed in this paper, which models the stable degradation stage and the accelerated degradation stage separately, and adjusts the decay rate in the accelerated stage by introducing a degradation ratio parameter α to better reflect the actual degradation law of the engine.

[0106] The experimental results are shown in Table 6. As can be seen from the results in Table 6, the two-stage degradation labeling scheme of this method achieves the best performance in both the Score function and the RSME index. Compared with the unified maximum life linear labeling method, the Score function decreases from 366.72 to 291.70, and the RSME index decreases from 16.94 to 14.23. Compared with the individualized maximum life linear labeling method, this scheme also shows better prediction accuracy. The results indicate that the two-stage degradation labeling scheme of this method can more accurately characterize the nonlinear degradation process of the engine, thereby effectively improving the stability and reliability of remaining life prediction.

[0107] Table 6

[0108] j. Comparison of Model Prediction Results with the Model To verify the predictive performance of the TPRUL-Net prediction model in this scheme, it was used to predict the remaining life of the complete engine and compared with the true label. Figure 13 , Figure 14 and Figure 15 As can be seen, the prediction error is smaller when the engine is close to failure because the system accumulates more degradation information over time. Furthermore, the breakpoints of the actual and predicted signals in the figure are very close, indicating that the prediction results match the actual degradation trend.

[0109] The above description is merely an example of a specific solution of the present invention. For any devices and structures not described in detail herein, it should be understood that they are implemented using common devices and methods already available in the art.

[0110] The above description is merely one embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting the remaining life of a turbofan engine based on two-stage degradation tags, characterized in that, Includes the following steps: S1. Acquire sensor data from the turbofan engine and perform preprocessing; S2. Construct differentiated features based on physical attributes in sensor data; S3. For sensor data, the optimal number of segments for each physical attribute sensor data is adaptively determined by combining piecewise linear fitting and elbow method, and the degradation inflection point of the turbofan engine as a whole is obtained by multi-sensor breakpoint fusion algorithm. S4. Construct a two-stage degradation label based on the degradation inflection point, wherein a stable degradation label is constructed before the degradation inflection point, and a nonlinear accelerated degradation label is constructed after the degradation inflection point. S5. Construct a TPRUL-Net prediction model that integrates a BiLSTM network and an attention mechanism. The TPRUL-Net prediction model is configured with a temporal feature branch for inputting differential features and two-stage degradation labels, and a handcrafted feature branch for inputting statistical features obtained from sensor data. The TPRUL-Net prediction model outputs the remaining lifetime prediction value with the fused features of the two branches. S6. Acquire sensor data of the turbofan engine under test, and use the TPRUL-Net prediction model to predict the remaining service life of the turbofan engine under test.

2. The method for predicting the remaining life of a turbofan engine based on a two-stage degradation tag, as described in claim 1, is characterized in that... In step S1, the step of acquiring and preprocessing the sensor data of the turbofan engine, the sensor data is time-series data, and the preprocessing includes: outlier removal and normalization.

3. The method for predicting the remaining life of a turbofan engine based on a two-stage degradation tag, as described in claim 1 or 2, is characterized in that... In step S2, the step of constructing differentiated features based on the physical attributes in the sensor data involves using proportional calculations to construct consistent change features that evolve over time for sensor data with physical attributes of pressure and flow, and using difference calculations to construct abnormal features that accumulate over time for sensor data with physical attributes of temperature and vibration. The sensor data is then enhanced based on the consistent change features and the abnormal features to construct differentiated features.

4. The method for predicting the remaining life of a turbofan engine based on a two-stage degradation tag, as described in claim 3, is characterized in that... In step S2, the step of constructing differentiated features based on the physical properties in the sensor data uses the sensor data of the first working cycle of the turbofan engine as the reference sensor data, and performs proportional or difference calculations on the sensor data of each subsequent working cycle and the reference sensor data to construct the corresponding features.

5. The method for predicting the remaining life of a turbofan engine based on a two-stage degradation tag, as described in claim 3, is characterized in that... Step S3, which involves adaptively determining the optimal number of segments for each physical attribute of the sensor data using a combination of piecewise linear fitting and the elbow method, and obtaining the overall degradation inflection point of the turbofan engine through a multi-sensor breakpoint fusion algorithm, includes: Principal component analysis was performed on the preprocessed sensor data, and a preset number of principal components were retained as PCA dimensionality reduction data. Low-pass filtering is applied to the PCA dimensionality reduction data to eliminate noise interference; Piecewise linear fitting is performed on the PCA dimensionality reduction data of the sensor after low-pass filtering. After completing piecewise linear fitting for different orders, the second-order residual sum of squares is calculated. Finally, the position corresponding to the minimum value of the second-order difference is found as the elbow turning point, and the optimal number of segments for the sensor data of each physical attribute is determined. The multi-sensor breakpoint fusion algorithm based on slope mutation calibration is used to filter the piecewise linear fitting results under the optimal number of segments to obtain the overall degradation inflection point of the turbofan engine.

6. The method for predicting the remaining life of a turbofan engine based on a two-stage degradation tag, as described in claim 5, is characterized in that... The step of obtaining the overall degradation inflection point of a turbofan engine by filtering the piecewise linear fitting results under the optimal number of segments using a multi-sensor breakpoint fusion algorithm based on slope mutation calibration includes: Based on the piecewise linear fitting results, the fitting breakpoints of each segment are obtained, and the effective breakpoints among the fitting breakpoints are selected. Cluster feature vectors are constructed based on the correlation coefficient. The correlation coefficient is obtained by calculating the absolute value of the Pearson correlation coefficient between the values ​​of the first and last two moments of the sensor data and the corresponding running cycle. K-means clustering was used to group similar valid breakpoints into several groups. After removing extreme values ​​from each group of valid breakpoints using the 3σ criterion, the groups were weighted and fused within each group using the correlation coefficient as the weight. For each effective breakpoint group after intra-group weighted fusion, the inter-group weights are calculated based on the average relevance and breakpoint consistency to complete the cross-group weighted fusion. If the number of effective breakpoints is less than the number of clusters, the fusion breakpoint is obtained directly by relevance weighted average as the degradation inflection point.

7. The method for predicting the remaining life of a turbofan engine based on a two-stage degradation tag, as described in claim 6, is characterized in that... In step S4, the step of constructing a two-stage degradation label based on the degradation inflection point, the stable degradation label is constructed based on a linear decay model, and the nonlinear accelerated degradation label is constructed by introducing an accelerated decay factor. Therefore, the constructed two-stage degradation label can be expressed as: in, Indicates a degradation label. This represents the total number of cycles of the turbofan engine within the observation period. This indicates the current cycle number of the turbofan engine. This indicates the turning point in the overall degradation of a turbofan engine. This indicates the rate of acceleration attenuation.

8. The method for predicting the remaining life of a turbofan engine based on a two-stage degradation tag, as described in claim 7, is characterized in that... The accelerated decay factor introduced by the nonlinear accelerated degradation label is obtained based on the following steps: The first average degradation slope of the turbofan engine is obtained by acquiring sensor data before the degradation inflection point. The second average degradation slope of the turbofan engine's nonlinear accelerated degradation is obtained from sensor data after the degradation inflection point. The degradation slope ratio of each sensor in the turbofan engine is obtained based on the second average degradation slope and the first average degradation slope. The average slope ratio of the turbofan engine is obtained based on the degradation slope ratio of each sensor, and the effective slope ratio range of the turbofan engine is obtained by expanding the average slope ratio. Based on the effective rate range of all turbofan engines, the interval is summarized to obtain the overall engine acceleration decay rate reference interval, and the value of the acceleration decay rate to be introduced is obtained by taking the value of the acceleration decay rate reference interval.

9. The method for predicting the remaining life of a turbofan engine based on a two-stage degradation tag, as described in claim 8, is characterized in that... In step S5, the step of constructing the TPRUL-Net prediction model that integrates BiLSTM network and attention mechanism, the TPRUL-Net prediction model includes: temporal feature branch, handmade feature branch, feature concatenation layer and output layer; The temporal feature branch includes: a first input layer, a BiLSTM network, an attention mechanism module, and a first linear layer; The first input layer is used to receive differential features and two-stage degradation labels and process them with a sliding time window to output a first feature tensor sequence with a fixed step size; The BiLSTM network captures degradation information based on forward and backward dependencies based on the first feature tensor sequence; The attention mechanism module generates attention weights in the time dimension based on the degradation information, highlights the feature contribution of degradation information at key moments, and uses residual connections to fuse the attention weights with the degradation information to generate temporal features. The first linear layer receives the temporal features and outputs them after flattening. The handcrafted feature branch includes: a second input layer, a statistical module, a Z-Score normalization layer, and a second linear layer; The second input layer is used to receive sensor data and process it with a sliding time window to output a second feature tensor sequence with a fixed step size; The statistical module extracts statistical features based on the second feature tensor sequence, wherein the statistical features include: mean, standard deviation, and degradation trend coefficient; The Z-Score normalization layer is used to receive statistical features and perform Z-Score standardization. The second linear layer receives the statistical features after Z-Score standardization and flattens them before outputting the result; The feature splicing layer receives temporal features output from the temporal feature branch and statistical features output from the manual feature branch, and splices them along the feature dimension to obtain a dual-branch fused feature; The output layer maps a single non-negative real number based on fused features, which serves as a prediction of the remaining lifespan of the turbofan engine.

10. The method for predicting the remaining life of a turbofan engine based on a two-stage degradation tag, as described in claim 1, 5, or 6, is characterized in that... The optimal number of segments is 5.

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