Method for Quantifying Uncertainty of Remaining Life of Aeroengine under Online Prediction Scenario

Abstract

The present invention relates to the technical field of aero-engines, and specifically relates to a method for quantifying the uncertainty of the remaining life of an aero-engine in an online prediction scenario. This method obtains a training data set during the test run and operation of the aero-engine; based on a diffusion model, according to the monitoring data, and in combination with a characterization mapping function, a denoising network model is obtained; test samples with randomly missing and sensor fault data are collected in the online prediction scenario; the filled samples are obtained according to the test samples through the optimized denoising network model; the filled samples and the test samples are combined to obtain the filled test samples; for the filled test samples, according to the trained RUL prediction model and the weighted empirical distribution function, a conformal prediction is used to construct an RUL prediction interval. The purpose of the present invention is to accurately evaluate the comprehensive performance of the aero-engine and improve the reliability and robustness of the prediction results.

Description

Technical Field

[0001] The present invention relates to the technical field of aero-engines, and particularly to a method for quantifying the uncertainty of the remaining life of an aero-engine in an online prediction scenario. Background Art

[0002] The reliability of an aero-engine is the basis for ensuring aviation safety, improving operation efficiency, and achieving economic feasibility. Due to the highly complex design and operation of an aero-engine, it is crucial to ensure its comprehensive performance. With the continuous progress of aviation technology, the need to ensure the continuous and safe operation of the engine is becoming increasingly urgent. Against this background, Prognostics and Health Management (PHM) has gradually become a key strategy. PHM aims to monitor, predict, and manage the health status and comprehensive performance of an aero-engine in real time by combining sensor monitoring, data acquisition, comprehensive performance control optimization, and maintenance decision-making models. Through proactive management, PHM not only improves the safety and reliability of the system, but also optimizes the maintenance plan, reduces downtime, and significantly reduces operating costs. In the optimization of aero-engine performance control and comprehensive performance evaluation, the Remaining Useful Life (RUL) refers to the time interval from the current moment to the expected occurrence of a failure. As one of the core indicators of PHM, RUL is an important parameter for quantitatively evaluating the change in the comprehensive performance of the engine, providing an important basis for the performance control, evaluation, and formulation of preventive maintenance decisions of an aero-engine.

[0003] In the prediction of aero-engine RUL, uncertainty quantification is an important method for evaluating the reliability and robustness of prediction results. It can not only provide a prediction interval to help decision-makers comprehensively evaluate the comprehensive performance and potential risks of an aero-engine, but also optimize the maintenance strategy and enhance the robustness of the prediction model. By quantifying the uncertainty of the prediction results, decision-makers can clarify the possible range of prediction errors, thereby achieving more precise performance control and optimization, and making more scientific and reliable decisions.

[0004] In recent years, deep learning methods have demonstrated powerful performance in the prediction of aero-engine RUL and can automatically extract deep degradation features from sensor monitoring data. In the prior art, deep learning methods are used to achieve prediction through a deterministic neural network, mainly providing a point estimate of RUL prediction. Although these methods have made significant progress in prediction performance, they have failed to effectively quantify the uncertainty of the prediction results, resulting in the inability to accurately evaluate the comprehensive performance of an aero-engine in a complex and changing actual operating environment.

[0005] In addition, in actual online prediction scenarios, especially in aeroengines operating under harsh working conditions, missing problems often occur in sensor monitoring data. These missing data mainly have two types: one is random data missing, and the other is complete data missing due to sensor failures. Random data missing is usually caused by reasons such as temporary sensor malfunctions, network transmission problems, or data storage failures. This missing pattern is usually intermittent and scattered. Different from this, the complete missing caused by sensor failures is more destructive because it can lead to the unavailability of entire segments of data from one or more sensors. Such missing not only seriously affects the integrity of the data but may also lead to incorrect assessments of the comprehensive performance and health status of aeroengines. The random missing and partial sensor failure problems in online prediction scenarios significantly affect the performance of existing deep learning-based RUL prediction methods. Summary of the Invention

[0006] To solve the above technical problems, the present invention mainly aims at the problems that existing deep learning methods cannot effectively quantify the uncertainty of prediction results in aeroengine RUL prediction, and the negative impacts of random missing and partial sensor failure data in online prediction scenarios on the performance of existing methods. The present invention provides a method for quantifying the uncertainty of the remaining useful life of aeroengines in an online prediction scenario, which aims to accurately evaluate the comprehensive performance of aeroengines and improve the reliability and robustness of prediction results.

[0007] The object of the present invention is to provide a method for quantifying the uncertainty of the remaining useful life of aeroengines in an online prediction scenario, including:

[0008] Obtain a training data set during the test run and operation of the aeroengine, where the training data set includes monitoring data and the remaining useful life labels corresponding to the monitoring data;

[0009] Obtain a characterization mapping function according to the characterization of the monitoring data through a pre-training strategy based on the monitoring data;

[0010] Based on the diffusion model, obtain a denoising network model according to the monitoring data and in combination with the characterization mapping function;

[0011] Divide the training data set into a training subset and a calibration subset;

[0012] Train a RUL prediction model according to the training subset to obtain a trained RUL prediction model;

[0013] Construct a mapping network that maps the monitoring data to the latent space through the calibration subset;

[0014] Collect test samples with random missing and sensor failure data in the online prediction scenario;

[0015] Obtain the filled samples through the optimized denoising network model according to the test samples; combine the filled samples with the test samples to obtain the filled test samples;

[0016] Map the samples in the calibration subset and the filled test samples into the latent space through the mapping network to obtain the weights of each sample in the calibration subset;

[0017] Construct a compliance score based on the absolute residuals of each sample in the calibration subset, and weight the compliance score with the weights of different samples to define a weighted empirical distribution function;

[0018] For the filled test samples, construct a RUL prediction interval through conformal prediction according to the trained RUL prediction model and the weighted empirical distribution function.

[0019] Preferably, the characterization mapping function is obtained according to the following steps:

[0020] Mask the monitoring data and use it as input to train the pre-trained model until convergence to obtain the trained pre-trained model; wherein, the pre-trained model sequentially includes an input encoding, a Transformer encoder, and a linear layer; remove the linear layer from the trained pre-trained model to obtain the characterization mapping function.

[0021] Preferably, the denoising network model is obtained according to the following steps:

[0022] Divide the monitoring data into two parts: the filling target and the observed values;

[0023] Encode the observed values through the characterization mapping function to obtain the first conditional information representation;

[0024] Based on the diffusion model, add Gaussian noise to the filling target to generate the noisy data; and use the noisy data and the first conditional information representation as the input of the denoising network model, and optimize the parameters of the denoising network model through the backpropagation and gradient descent algorithms to obtain the optimized denoising network model.

[0025] Preferably, in the process of obtaining the filled samples, it includes:

[0026] Generate initial Gaussian noise samples according to the position of each missing value in the test samples, and gradually remove the noise through the reverse generation process based on the optimized denoising network model to obtain the filled samples.

[0027] Preferably, in the process of obtaining the filled samples, it further includes:

[0028] Encode the test samples through the characterization mapping function to obtain the second conditional information representation;

[0029] Each step in the reverse generation uses the second conditional information representation as the input to the optimized denoising network model.

[0030] Preferably, when combining the filled samples with the test samples, it includes: filling the filled samples into the positions of the missing values corresponding to the test samples to obtain the filled test samples.

[0031] Preferably, calibrating the absolute residuals of each sample in the calibration subset includes:

[0032] Obtaining the prediction results for each sample in the calibration subset through the trained RUL prediction model;

[0033] Obtaining the absolute residuals of each sample in the calibration subset according to the actual results and the prediction results of each sample in the calibration subset.

[0034] Preferably, defining the mapping network that maps the monitoring data to the latent space includes: defining a triple network model composed of three mapping networks with shared weights;

[0035] Constructing the training samples from the calibration subset including anchor samples, positive samples, and negative samples to train the triple network model to obtain the trained mapping network.

[0036] Preferably, when constructing the training samples from the calibration subset including anchor samples, positive samples, and negative samples, it includes: selecting an anchor sample from the calibration subset; selecting multiple neighbors with the closest absolute residual distance to the anchor sample as positive samples, and the remaining samples as negative samples.

[0037] Preferably, the RUL prediction model is composed of an LSTM layer, a Dropout layer, a GELU activation function, and a linear layer.

[0038] The present invention has at least the following beneficial effects:

[0039] The present invention provides a method for quantifying the uncertainty of the remaining useful life of an aero-engine in an online prediction scenario. This method effectively captures the representation of the sensor monitoring data of the aero-engine in the online prediction scenario through a pre-training strategy. Based on this strategy, a self-supervised learning task is designed to train a diffusion model to fit the distribution of randomly missing and partially faulty sensor data, thereby achieving efficient and reliable data filling. This method can significantly improve the integrity of the data, ensure accurate RUL prediction even in the case of missing data, and enhance the robustness of the comprehensive performance evaluation of the aero-engine.

[0040] The present invention introduces a residual pattern recognition method based on deep metric learning, which weights the conformity scores of conformal prediction according to the distances of input data in the latent space, thereby constructing a more accurate and reliable remaining useful life (RUL) prediction interval for aeroengines and achieving an accurate assessment of the comprehensive performance of aeroengines. In addition, the construction process of this prediction interval does not depend on specific data distributions or model assumptions, and can flexibly adapt to existing RUL prediction models based on deep learning. Description of the Drawings

[0041] Figure 1 It is a flowchart of the technical solution of the present invention.

[0042] Figure 2 It is an architecture diagram of the pre-trained model of the present invention.

[0043] Figure 3 It is an architecture diagram of the denoising network model of the present invention.

[0044] Figure 4 It is a schematic diagram of the self-supervised training of the diffusion model of the present invention.

[0045] Figure 5 It is an architecture diagram of the RUL prediction model of the present invention.

[0046] Figure 6 It is an architecture diagram of the triplet network model of the present invention.

[0047] Figure 7 It is an effect diagram of the RUL prediction interval of the test engine under data missing situation 1 in subset FD001 of the present invention.

[0048] Figure 8 It is an effect diagram of the RUL prediction interval of the test engine under data missing situation 2 in subset FD001 of the present invention.

[0049] Figure 9 It is an effect diagram of the RUL prediction interval of the test engine under data missing situation 3 in subset FD001 of the present invention.

[0050] Figure 10 It is an effect diagram of the RUL prediction interval of the test engine under data missing situation 4 in subset FD001 of the present invention. Detailed Embodiments

[0051] In order to elaborate on the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following will be described in detail in combination with embodiments.

[0052] The present invention addresses the problem that existing deep learning methods cannot effectively quantify the uncertainty of prediction results in the RUL prediction of aeroengines, as well as the negative impact of randomly missing and partially sensor-faulty data on the performance of existing methods in the online prediction scenario. The objective of the present invention is to provide a method for quantifying the uncertainty of the remaining useful life of aeroengines in an online prediction scenario, which aims to accurately evaluate the comprehensive performance of aeroengines and improve the reliability and robustness of prediction results.

[0053] See Figure 1 As shown, a method for quantifying the uncertainty of the remaining useful life of aeroengines in an online prediction scenario mainly includes: (1) Representation learning based on a pre-training strategy, obtaining the representation of sensor monitoring data through the pre-training strategy to provide effective feature input for subsequent distribution fitting tasks; (2) Distribution fitting based on a diffusion model, that is, training a diffusion model by constructing a self-supervised learning task to fit the distribution of randomly missing and partially faulty sensor data in the online prediction scenario; (3) Residual pattern recognition based on deep metric learning, mainly identifying the residual patterns in RUL prediction through deep metric learning, mapping input data with similar residuals to the latent space so that these data are close to each other in this space, while input data with dissimilar residuals are far from each other in this space; (4) Construction of the RUL prediction interval based on conformal prediction; (5) Online prediction: For aeroengine test samples with randomly missing and partially sensor-faulty data in the online prediction scenario, data filling is performed through a distribution fitting method to obtain complete sensor monitoring data; according to the distance of the input data in the latent space, the conformity scores of conformal prediction are weighted to construct the RUL prediction interval of the test sample, accurately quantifying the uncertainty of the prediction result to achieve an accurate evaluation of the comprehensive performance of aeroengines.

[0054] To achieve the above objective, a method for quantifying the uncertainty of the remaining useful life of aeroengines in an online prediction scenario includes:

[0055] S1. Obtain the training data set of the aeroengine during the test run and operation, where the training data set includes monitoring data and the remaining useful life label corresponding to the monitoring data;

[0056] Specifically, obtain the monitoring data of the aeroengine during the test run and operation; preprocess the monitoring data to obtain the training data set; where the training data set includes monitoring data and the remaining useful life label corresponding to the monitoring data;

[0057] In the aero-engine system, first, key sensors such as temperature, pressure, and rotational speed are correctly installed and connected. Then, parameters such as the data transmission method, sampling frequency, and data storage format of the sensors are configured to ensure that the sensors can work properly and collect data stably. Through these sensors, the monitoring data of the aero-engine is continuously recorded, and the collected data is effectively stored. Further, the Min-Max normalization method is used to normalize the collected sensor monitoring data to eliminate the influence between different dimensions and ensure that various data can be compared and analyzed on a unified scale. At the same time, the sliding window technique is used to accurately capture the data correlation between adjacent time points, and the sensor monitoring data is converted into the required sample size to construct a training dataset . Among them, represents N the sensor monitoring data of an engine running to failure, and represents the remaining useful life label corresponding to

[0058] The monitoring data of the th engine is expressed as , where represents the total number of monitoring time steps of the th engine from operation to failure, represents the sampling data at the th time step in K , and

[0059] is the total number of monitoring sensors. In this embodiment, the training dataset is complete and does not contain any missing data. Let represent the aero-engine test sample in the online prediction scenario, which has two types of data missing, namely random missing and partial sensor failures. Assume that the proportion of random data missing is .

[0060] The present invention aims to construct a prediction model through the training dataset and perform uncertainty quantification of the remaining useful life (RUL) prediction for the aero-engine test sample with random missing and partial sensor failure data in the online prediction scenario.

[0061] S2. Obtain a representation mapping function according to the representation of the monitoring data through a pre-training strategy based on the monitoring data;

[0062] The representation mapping function is obtained according to the following steps:

[0063] The monitored data is masked and used as input to train the pre-trained model until convergence to obtain a trained pre-trained model. Among them, the pre-trained model sequentially includes an input encoding, a Transformer encoder, and a linear layer. The trained pre-trained model has the linear layer removed to obtain a characterization mapping function.

[0064] In this embodiment, the sensor monitoring data is masked to obtain masked data , which is used as the input of the pre-trained model. The specific steps of masking are as follows:

[0065] First, the masking ratios for random dropout and sensor faults are respectively set to and ;

[0066] Furthermore, for each sample in the sensor monitoring data , a random dropout mask matrix and a sensor fault mask matrix are generated, where L represents the total number of monitoring time steps of , K represents the total number of monitoring sensors, and the mask values , . In the mask matrix , the mask value is generated through a Bernoulli distribution . In the mask matrix , sensors are randomly selected. Suppose the index set of these sensors is D . For all j belonging to D , the mask values of all time steps of this sensor are set to 0; conversely, the mask value is set to 1. Considering both the random dropout mask matrix and the sensor fault mask matrix , a comprehensive mask matrix is generated, where represents the logical AND operation of the corresponding elements of the matrices and ;

[0067] Furthermore, the sensor monitoring data is multiplied by the corresponding elements of the comprehensive mask matrix to obtain the masked monitoring data , that is, , where Indicates element-wise multiplication at the corresponding positions. The masked data will be used as the input to the pre-trained model.

[0068] See Figure 2 As shown, the architecture of the pre-trained model mainly consists of three parts: input encoding, Transformer encoder, and linear layer. First, the sensor monitoring data after masking is used as the input to the model and undergoes input encoding. The input encoding is implemented through 1×8 and K ×1 convolutional layers to extract local temporal features and correlations between variables. Specifically, M 1×8 temporal convolutional filters are applied to the input data to extract temporal patterns. Then, through a number of K ×1 spatial convolutional filters perform a second convolution on the output of the temporal convolution to capture the correlations between variables in the sensor data and construct an input embedding with a dimension of . Next, layers of Transformer encoder capture complex spatio-temporal dependencies in the data through multi-head attention mechanism, feed-forward neural network, and normalization layer. Finally, the encoded representation passes through the linear layer to generate the prediction results of the masked values .

[0069] The optimization objective of the pre-trained model is to minimize the mean squared error between the predicted value and the true value . The loss function is defined as follows:

[0070]

[0071] where, N represents the total number of samples in the sensor monitoring data , represents the set of positions of all masked values in , represents the number of elements in the set . Then, the model parameters are optimized through backpropagation and gradient descent algorithms to minimize the loss function

[0072] After the model pre-training is completed, the linear layer is removed and a representation mapping functionis constructed to obtain the sample representation , where is the dimension of the sample representation.

[0073] S3. Based on the diffusion model, according to the monitoring data and combined with the representation mapping function, a denoising network model is obtained;

[0074] The denoising network model is obtained according to the following steps:

[0075] Divide the monitoring data into two parts: the filling target and the observed value;

[0076] Encode the observed value through a feature mapping function to obtain the first conditional information representation;

[0077] Based on the diffusion model, add Gaussian noise to the filling target to generate noisy data; and use the noisy data and the first conditional information representation as the input of the denoising network model, and optimize the parameters of the denoising network model through backpropagation and gradient descent algorithms to obtain the optimized denoising network model.

[0078] It should be noted that since the true labels of the missing data in the online prediction scenario cannot be obtained, in this embodiment, a self-supervised learning task is constructed through the complete sensor monitoring data in the training dataset to train the diffusion model to fit the distribution of randomly missing and partially faulty sensor data, so as to achieve effective data filling. The diffusion model is a generative model designed to learn the high-dimensional and complex distribution of data and generate new samples. Its core idea is to gradually transform the data into noise through the forward diffusion process, and then reconstruct the data distribution from the noise and generate new samples through the reverse generation process.

[0079] In this embodiment, use to represent a complete monitoring data sample in the training dataset, and divide it into two parts: the observed value and the filling target . The method of data division is similar to the masking processing method described in S2. By generating a comprehensive mask matrix , the observed value and the filling target can be determined, where represents element-wise multiplication at the corresponding positions. The training objective of the diffusion model is to fit the distribution of the filling target , assuming its distribution is .

[0080] In the forward diffusion process, gradually add Gaussian noise to the filling target . This process can be represented by a Markov chain containing T time steps:

[0081]

[0082] Among them, in represents from time step 1 to TMarkov transitions. The noisy data also follows a Gaussian distribution:

[0083]

[0084] where and represent the mean and covariance of the Gaussian distribution, respectively;

[0085] , , is an adjustable hyperparameter used to control the noise level added in each diffusion process. After T steps of diffusion, 's distribution will ultimately be perturbed into a standard Gaussian distribution .

[0086] In the reverse generation process, sample from the standard Gaussian distribution , and then gradually denoise it to reconstruct the distribution of the filling target . To make full use of the information of the observed value , encode it through the characterization mapping function constructed in S2 to obtain the first conditional information characterization . Then, introduce as the generation conditional information into the reverse generation process. The reverse generation process can be represented as the following Markov chain:

[0087]

[0088] where in represents the Markov transition from time step to , is a parameterized model through which Gaussian noise is gradually removed. This parameterized model also follows a Gaussian distribution:

[0089]

[0090] whose mean and covariance are shown as follows, respectively:

[0091]

[0092]

[0093] where ; ;

[0094] ; .

[0095] is a denoising network, a neural network model that represents through conditional information , time steps t and the noisy data at that time step to predict Gaussian noise .

[0096] See Figure 3 as shown, the overall architecture of the denoising network model, where the specific dimensions of each output tensor are marked. Figure 3 In B represents the batch size of training samples, C represents the number of residual channels of the network, K represents the total number of monitoring sensors (spatial dimension), L represents the total number of time steps (time dimension). Specifically, the denoising network consists of residual layers with residual channels C stacked. The core of each residual layer is the time - space attention mechanism, which processes tensor inputs with dimensions and respectively by introducing two Transformer encoders with different encoding directions to capture the temporal and spatial dependencies in the multivariate sensor monitoring data. In addition, to achieve efficient feature extraction, a 1×1 convolutional layer is further introduced in each residual layer, and the nonlinear representation ability of the network is enhanced through a gated activation layer. For residual layer 1, its main input is the noisy data , which is processed by a 1×1 convolutional layer and a GELU activation function and then input into residual layer 1. For each subsequent residual layer, the output of the previous residual layer is used, and the residual connection of the previous residual layer is combined as its main input. In addition, each residual layer also receives two additional inputs, namely the information of the diffusion time step t and the conditional information representation , and these additional inputs are processed through a linear layer and a GELU activation function. For each diffusion time step , an encoding vector with a dimension of is used as the embedding of the current time step. The calculation method of this encoding vector can be expressed as , , where . Finally, the skip connections of all residual layers are added together, and then processed through a 1×1 convolutional layer, a normalization layer, and a GELU activation function to generate the final noise prediction result.

[0097] Furthermore, the diffusion model is trained by solving the following optimization problem, and the optimization objective is to make the prediction result of the denoising network as close as possible to the actually added Gaussian noise , and optimize the parameters of the denoising network model through backpropagation and gradient descent algorithms:

[0098]

[0099] See Figure 4 As shown, the self-supervised training process of the diffusion model is summarized as follows: First, divide the complete monitoring data in the training set into observed values and filling targets , and encode the observed values through the feature mapping function constructed in S2 to obtain the first conditional information representation . Then, according to the given noise level , add Gaussian noise to the filling target to generate the noisy data , where , . At this time, the noisy data , the first conditional information representation and the time step t constitute the input of the denoising network , so as to predict the Gaussian noise t added at the time step . Finally, minimize the loss function , and optimize the parameters of the denoising network model through backpropagation and gradient descent algorithms , that is, obtain the optimized denoising network model

[0100] S4. Divide the training data set into a training subset and a calibration subset;

[0101] Train the RUL prediction model according to the training subset to obtain the trained RUL prediction model;

[0102] Construct a mapping network that maps the monitoring data to the latent space through the calibration subset;

[0103] The above-defined mapping network that maps the monitoring data to the latent space includes: defining a triple network model composed of three mapping networks with shared weights;

[0104] Construct training samples from the calibration subset including anchor samples, positive samples and negative samples to train the triple network model, and obtain the trained mapping network

[0105] When constructing the training samples for the calibration subset to include anchor samples, positive samples, and negative samples, it includes: selecting an anchor sample from the calibration subset; selecting multiple neighbors with the closest absolute residual distance to the anchor sample as positive samples, and the remaining samples as negative samples.

[0106] The RUL prediction model consists of an LSTM layer, a Dropout layer, a GELU activation function, and a linear layer, as shown in Figure 5 shown.

[0107] The present invention identifies the residual pattern in RUL prediction through deep metric learning, maps the input data with similar residuals to the latent space, makes these data close to each other in this space, and makes the input data with dissimilar residuals far from each other in this space.

[0108] In this embodiment, the training data N containing samples is divided into two subsets:

[0109] Training subset and calibration subset where .

[0110] By training an RUL prediction model which maps the input feature space to the output space , and solves the RUL prediction task by minimizing the mean squared error loss function. It should be emphasized that it can be based on the existing RUL prediction models based on deep learning methods. is then used for deep metric learning to identify the residual pattern of RUL prediction and is also used for conformal prediction to construct the prediction interval.

[0111] Applying the trained to to obtain the prediction result , and calculating the absolute residual where . In addition, removing the last linear layer of to construct the embedding function where is the dimension of the embedding.

[0112] Furthermore, through the continuous triple construction method, training sample pairs are constructed, including anchor samples , positive samples and negative samples : For a given mini-batch training sample set, select an anchor sample , and select the nearest k number of neighbors as the positive sample set . The remaining samples are used as the negative sample set . Then, construct all possible sample pairs from the positive and negative sample sets , and combine them with the anchor sample to form triplets to ensure that the model can observe as diverse triplets as possible during training.

[0113] Deep metric learning maps sensor monitoring data to a latent space through a triplet network model. The triplet network model consists of three sub-networks with shared weights , as shown in Figure 6 . Each sub-network receives the anchor sample , positive sample and negative sample as inputs, and performs feature extraction through LSTM layers and Dropout layers. The extracted features are then stacked with the corresponding sample embeddings , and to obtain feature information related to the remaining useful life. Finally, the features are further processed through linear layers and Dropout layers, and non-linear information is introduced through the GELU activation function to map the input data to the latent space and generate sample representations , and in the latent space.

[0114] Furthermore, the triplet network model is trained through the Log-ratio loss function, and the definition of the Log-ratio loss function is as follows:

[0115]

[0116] where represents the Euclidean distance, and , and represent the absolute residuals of the anchor sample, positive sample, and negative sample, respectively. After the triplet network model is trained, the mapping network is obtained to map the input data sample points to the latent space. In this latent space, the Euclidean distance between points reflects the similarity of their absolute residuals, thus achieving effective residual pattern recognition.

[0117] S5. Collect test samples with randomly missing and sensor fault data in the online prediction scenario;

[0118] Obtain a filled sample through the optimized denoising network model according to the test sample; combine the filled sample with the test sample to obtain the filled test sample.

[0119] During the process of obtaining the filled sample, it includes:

[0120] Generate an initial Gaussian noise sample according to the position of each missing value in the test sample, and gradually remove the noise through the reverse generation process based on the optimized denoising network model to obtain the filled sample.

[0121] During the process of obtaining the filled sample, it also includes:

[0122] Encode the test sample through the characterization mapping function to obtain the second conditional information characterization.

[0123] In each step of the reverse generation, use the second conditional information characterization as the input of the optimized denoising network model.

[0124] When combining the filled sample with the test sample, it includes: filling the filled sample into the position of the corresponding missing value in the test sample to obtain the filled test sample.

[0125] For the aero-engine test samples with random missing values and partial sensor fault data in the online prediction scenario, the present invention fills the data through the distribution fitting method to obtain complete sensor monitoring data.

[0126] In this embodiment, take the test sample with random missing values and sensor fault data in the online prediction scenario as the observed value , and encode it through the characterization mapping function constructed in S2 to obtain the second conditional information characterization .

[0127] For each missing value position, generate an initial Gaussian noise sample , and gradually remove the noise through the reverse generation process. In each step of the generation process, use the second conditional information characterization as the conditional input to generate an estimate of the missing value, which can be specifically expressed as:

[0128]

[0129] where, ; ; ; ; ; is the given noise level.

[0130] is the denoising network model completed in training in S3. After multiple iterations, the final filling result is obtained . By combining and , the monitoring data of aero-engine sensors in a complete online prediction scenario is obtained .

[0131] S6. Map the samples in the calibration subset and the filled test samples through the mapping network into the latent space to obtain the weights of each sample in the calibration subset;

[0132] Construct a compliance score based on the absolute residual of each sample in the calibration subset, and weight the compliance score by the weights of different samples to define a weighted empirical distribution function;

[0133] The absolute residual of each sample in the calibration subset includes:

[0134] Obtain the prediction result of each sample in the calibration subset through the trained RUL prediction model;

[0135] Obtain the absolute residual of each sample in the calibration subset according to the actual result and the prediction result of each sample in the calibration subset.

[0136] In this embodiment, for the samples in the calibration subset and the filled test samples in the online prediction scenario , according to the mapping network obtained in S4 , map these samples into the latent space and calculate the weights of each sample in the calibration subset :

[0137]

[0138] wherein,

[0139] ,

[0140] represents the Euclidean distance. The weight reflects the similarity in the absolute residual of RUL prediction between the calibration sample and the test sample . The larger the weight , the more similar their absolute residuals are, indicating that the corresponding calibration sample is more important for generating the prediction interval of the test sample; on the contrary, it indicates that the difference in absolute residuals is greater, and the corresponding calibration sample has no reference value for generating the prediction interval of the test sample. In other words, if the test sample If it is closer to some samples in the calibration subset in the residual mode, then these calibration samples will be assigned higher weights.

[0141] According to the calibration subset Construct a compliance score based on the set of absolute residuals of the samples in , and weight the compliance score through the weights of different samples to define a weighted empirical distribution function :

[0142]

[0143] where , when , the value is 1, otherwise it is 0. Since the residual of the test sample is unknown, therefore uses in its definition to cover the possible residual values of new samples, that is , .

[0144] S7. For the filled test samples, according to the trained RUL prediction model and the weighted empirical distribution function, conformal prediction constructs the RUL prediction interval.

[0145] In this embodiment, according to the distance of the input data in the latent space, the compliance score of conformal prediction is weighted to construct the RUL prediction interval of the test sample, accurately quantifying the uncertainty of the prediction result to achieve an accurate assessment of the comprehensive performance of the aero-engine.

[0146] For the filled test samples in the online prediction scenario , the RUL prediction interval constructed by conformal prediction can be expressed as:

[0147]

[0148] where represents the RUL prediction model trained through the training subset ; represents the quantile of the weighted empirical distribution function , is the confidence level parameter.

[0149] This prediction interval construction method constructs the prediction interval by dividing the dataset and calculating the quantiles of the residuals, without relying on specific data distributions or model assumptions, so as to be able to flexibly adapt to the existing RUL prediction models based on deep learning. By analyzing the RUL prediction interval, an accurate assessment of the comprehensive performance of the aero-engine is achieved.

[0150] To further illustrate a method for quantifying the uncertainty of the remaining useful life of an aero-engine in an online prediction scenario, specific embodiments are used for illustration.

[0151] In this embodiment, the aero-engine sensor monitoring dataset C-MAPSS provided by NASA is used as a benchmark to verify the technical solution of the present invention. The C-MAPSS dataset simulates the operation process of an aero-engine under different operating conditions and fault modes and contains four subsets as shown in Table 1.

[0152] Table 1 Details of the C-MAPSS dataset

[0153]

[0154] Each subset contains training engine and test engine data. In this embodiment, a prediction model is constructed using the training engine data in the subset, and the uncertainty quantification of the remaining useful life (RUL) prediction for the test engine in the online prediction scenario is performed. In the online prediction scenario, in order to more comprehensively evaluate the prediction effect of the model under different data missing patterns of random missing and sensor faults, four data missing situations are set for the test engines in the C-MAPSS dataset, which are respectively set as Situation 1: random missing ratio , sensor fault ratio ; Situation 2: random missing ratio , sensor fault ratio ; Situation 3: random missing ratio , sensor fault ratio ; Situation 4: random missing ratio , sensor fault ratio . When performing the uncertainty quantification of the RUL prediction, the present invention sets the confidence level , that is, it is required that the constructed prediction interval satisfies a 90% coverage rate.

[0155] It should be noted that the present invention evaluates the performance of the model in RUL prediction through the root mean square error (RMSE) and the scoring function (Score). The smaller the RMSE and Score values, the better the RUL prediction effect of the model. In addition, the present invention also evaluates the performance of the model in uncertainty quantification in RUL prediction through the prediction interval coverage probability (PICP), the normalized average width of the prediction interval (PINAW), and the coverage width criterion (CWC). Specifically, the larger the PICP value, the higher the coverage probability of the prediction interval, and the more reliable the model is in uncertainty quantification; the smaller the PINAW value, the narrower the average width of the prediction interval, indicating that the model is more accurate in quantifying uncertainty; CWC is an index comprehensively evaluating the quality of the prediction interval. The larger the CWC value, the higher the quality of the prediction interval, and the model can more effectively balance the width and coverage probability of the prediction interval, thereby improving the accuracy and reliability of the prediction interval.

[0156] Table 2 shows the effects of the method proposed in this embodiment on the RUL prediction and uncertainty quantification of the test engine under different data missing scenarios.

[0157] Table 2 RUL prediction and uncertainty quantification effects under different data missing scenarios in the C-MAPSS dataset

[0158]

[0159] As can be seen from Table 2, as the data missing ratio increases, the overall RUL prediction effect of the model remains stable, and there is no significant decline in the prediction performance due to the increase in the data missing ratio. At the same time, despite the data missing, the model can still maintain a high PICP value. Especially when the data missing ratio is low, its PICP performance is close to that of the complete data, indicating that the model can still reliably quantify the uncertainty of the prediction results and ensure the coverage probability of the prediction interval in the case of data missing. In terms of PINAW and CWC, as the data missing ratio increases, the width of the prediction interval always remains within a reasonable range. In addition, the CWC value always maintains a high level, indicating that the model performs excellently in balancing the width and coverage probability of the prediction interval and can generate high-quality prediction intervals.

[0160] Generally speaking, the method proposed in the present invention demonstrates excellent robustness and high precision when dealing with randomly missing and partially faulty sensor data in the online prediction scenario, ensuring the coverage probability and width of the prediction interval during the uncertainty quantification process, and reflecting its significant advantages in accuracy and reliability.

[0161] To more intuitively demonstrate the effectiveness of the method proposed by the present invention in RUL prediction and uncertainty quantification, in subset FD001, the RUL prediction intervals for all test engines under different data missing scenarios were visualized, and the results are as follows Figures 7 to 10 shown. In the figure, the abscissa represents the serial numbers of the test engines, arranged in ascending order of the true RUL values; the ordinate is the RUL value. The curves in the figure represent the true RUL values of the engines, the squares represent the predicted values, and the vertical lines on both sides of the squares represent the corresponding prediction intervals. From Figure 7 it can be seen that most of the true RUL values are successfully covered by the prediction intervals, indicating that the model has high reliability in uncertainty quantification. At the same time, the model shows significant self - adaptability: for points with smaller prediction errors, the prediction intervals are narrower, reflecting the accuracy of the model at high confidence levels; for points with larger prediction errors, the prediction intervals are relatively wider to better cover the actual values. This self - adaptability highlights the advantage of the method proposed by the present invention in uncertainty quantification: when the model is more certain about the prediction result, the prediction interval shrinks; while when the uncertainty is higher, the interval expands appropriately to ensure that the true value can be covered. From Figure 8 , Figure 9 and Figure 10 it can be known that as the data missing ratio increases, the model still maintains the adaptive adjustment of the prediction intervals. For points with smaller prediction errors, the prediction intervals are still narrower, while for points with larger errors, the prediction intervals are wider.

[0162] In summary, when the data missing is less, the method proposed by the present invention can provide accurate and reliable prediction intervals; as the data missing ratio increases, although the prediction intervals become wider and the coverage rate decreases slightly, overall, the model still shows high reliability. This indicates that the method proposed by the present invention can effectively balance the accuracy and reliability of the prediction intervals under different degrees of data missing, demonstrating good practicability and robustness.

[0163] Based on the accurate and reliable RUL prediction intervals, the comprehensive performance of aero - engines can be comprehensively and scientifically evaluated. When the RUL predicted value is large and the prediction interval is narrow, it indicates that the expected life of the engine is long and the prediction uncertainty is low. In this case, it can be determined that its comprehensive performance is relatively good and the health state is stable. For example, in Figure 7Among them, for the engine with serial number 87 under data loss scenario 1 of subset FD001, its RUL predicted value is 120, and the prediction interval is [112, 129]. Since the RUL predicted value is relatively high and the confidence interval is relatively narrow, it indicates that the health state of this engine is relatively stable, the operation reliability is relatively strong, and the comprehensive performance is relatively excellent. However, when the RUL predicted value is large but the prediction interval is wide, although the expected life of the engine is long, due to the high prediction uncertainty, it is impossible to make a clear assessment of its comprehensive performance. In this case, vigilance should be maintained for the health state of the engine, and the maintenance window should be reasonably planned. For example, in Figure 7 Among them, for the engine with serial number 11, its RUL predicted value is 41, and the prediction interval is [13, 68]. Although its expected life seems sufficient, the large uncertainty indicates a relatively high uncertainty in its operating state. Therefore, this engine needs to be monitored intensively, and a maintenance strategy should be formulated in advance to reduce the operation risk. For an engine with a small RUL predicted value and a narrow prediction interval, it can be clearly determined that its comprehensive performance is poor, and its health state has entered an abnormal stage, and maintenance needs to be arranged immediately. For example, Figure 7 For the engine with serial number 6 in [reference], its RUL predicted value is 8, and the prediction interval is [3, 13]. Since its expected life is significantly insufficient and the prediction uncertainty is relatively low, it can be determined that its operating ability can no longer meet the normal requirements. Therefore, maintenance measures should be implemented as soon as possible to prevent potential failures and ensure the safety and reliability of system operation. Through the above analysis, it can be seen that the comprehensive performance evaluation of aero-engines based on the RUL prediction interval can not only provide accurate health state determination for decision-makers, but also effectively identify potential risks and optimize maintenance strategies, thereby improving the scientific nature and implementation efficiency of health management and maintenance decision-making.

[0164] The method proposed in the present invention performs excellently in dealing with random missing and partial faulty sensor data in the online prediction scenario, demonstrating high precision and strong robustness in the uncertainty quantification of aero-engine RUL prediction. In addition, this method has distribution independence and model independence, can flexibly adapt to existing RUL prediction models based on deep learning, provide accurate and reliable prediction intervals, and thus realize the accurate evaluation of the comprehensive performance of aero-engines, providing important support for health management and maintenance decision-making.

[0165] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for quantifying uncertainty of remaining life of an aircraft engine in an online prediction scenario, characterized in that: include: Acquire a training data set of an aircraft engine during a test run and operation process, wherein the training data set includes monitoring data and a remaining life label corresponding to the monitoring data; Characterize the monitoring data through a pre-training strategy according to the monitoring data to obtain a representation mapping function; Based on the diffusion model, according to the monitoring data and combined with the characterization mapping function, a denoising network model is obtained; Divide the training data set into a training subset and a calibration subset; The RUL prediction model is trained according to the training subset to obtain a trained RUL prediction model; A mapping network that maps monitoring data to latent space is constructed through the calibration subset; Collect test samples with random missing and sensor failure data in online prediction scenarios; Obtain a filled sample according to the test sample through the optimized denoising network model; combine the filled sample with the test sample to obtain a filled test sample; The samples in the calibration subset and the padded test samples are mapped to the latent space through the mapping network to obtain the weight of each sample in the calibration subset; Construct a conformity score based on the absolute residual of each sample in the calibration subset, and weight the conformity scores by the weights of different samples to define a weighted empirical distribution function; For the filled test samples, the RUL prediction interval is constructed by conformal prediction based on the trained RUL prediction model and the weighted empirical distribution function.

2. The method for quantifying uncertainty of remaining life of an aircraft engine in an online prediction scenario according to claim 1 is characterized in that: The characterization mapping function is obtained according to the following steps: The monitoring data is masked and used as input, and the pre-trained model is trained until convergence to obtain a trained pre-trained model; wherein the pre-trained model includes input encoding, Transformer encoder and linear layer in sequence; the linear layer is removed from the trained pre-trained model to obtain the representation mapping function.

3. The method for quantifying uncertainty of remaining life of an aircraft engine in an online prediction scenario according to claim 1 is characterized in that: The denoising network model is obtained according to the following steps: The monitoring data is divided into two parts: filling targets and observation values; Encoding the observed value through a representation mapping function to obtain a first conditional information representation; Based on the diffusion model, Gaussian noise is added to the filling target to generate noisy data; The noisy data and the first conditional information representation are used as the input of the denoising network model, and the parameters of the denoising network model are optimized through back propagation and gradient descent algorithms to obtain the optimized denoising network model.

4. The method for quantifying uncertainty of remaining life of an aircraft engine in an online prediction scenario according to claim 1, characterized in that: The filling sample acquisition process includes: An initial Gaussian noise sample is generated according to each missing value position in the test sample. Based on the optimized denoising network model, the noise is gradually removed through the reverse generation process to obtain the filling sample.

5. The method for quantifying uncertainty of remaining life of an aircraft engine in an online prediction scenario according to claim 4 is characterized in that: The filling sample acquisition process also includes: Encoding the test sample through a representation mapping function to obtain a second conditional information representation; Each step in the reverse generation takes the second conditional information representation as the input of the optimized denoising network model.

6. The method for quantifying uncertainty of remaining life of an aircraft engine in an online prediction scenario according to claim 4 is characterized in that: The combining of the filling sample with the test sample includes: filling the filling sample into the position of the missing value corresponding to the test sample to obtain the filled test sample.

7. The method for quantifying uncertainty of remaining life of an aircraft engine in an online prediction scenario according to claim 1, characterized in that: The absolute residual for each sample in the calibration subset includes: Each sample in the calibration subset is passed through the trained RUL prediction model to obtain the prediction result; Obtain the absolute residual for each sample in the calibration subset based on the actual result and the predicted result for each sample in the calibration subset.

8. The method for quantifying uncertainty of remaining life of an aircraft engine in an online prediction scenario according to claim 7 is characterized in that: The defining of a mapping network for mapping monitoring data to a latent space includes: defining a triplet network model consisting of three mapping networks sharing weights; The calibration subset is used to construct training samples including anchor samples, positive samples and negative samples to train the triplet network model and obtain a trained mapping network.

9. The method for quantifying uncertainty of remaining life of an aircraft engine in an online prediction scenario according to claim 8, characterized in that: When constructing the training samples of the calibration subset including anchor samples, positive samples and negative samples, the method includes: selecting an anchor sample from the calibration subset; selecting multiple neighbors with the closest absolute residual distance to the anchor sample as positive samples, and the remaining samples as negative samples.

10. The method for quantifying uncertainty of remaining life of an aircraft engine in an online prediction scenario according to claim 1, characterized in that: The RUL prediction model consists of an LSTM layer, a Dropout layer, a GELU activation function and a linear layer.

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