Residual service life prediction method and system based on deep Gaussian process and meta-learning, medium and equipment

Abstract

The invention relates to the field of machine learning, in particular to a residual service life prediction method and system based on a deep Gaussian process and meta-learning, a medium and equipment, and the method comprises the steps: obtaining original data to construct a multi-task data set; a multi-layer depth Gaussian process model is constructed based on a multi-task data set, a radial basis function kernel is used as a covariance function, and a multi-task Gaussian likelihood function is used for modeling uncertainty of RUL prediction; meta-training is carried out on a PHM data set, the model is optimized through internal circulation and external circulation, and an Adam optimizer is adopted to learn cross-task generalization weights; transferring the last layer of parameters and likelihood function parameters obtained by meta-training to a fan gearbox data set and an NASA aero-engine data set based on the same meta-learning model framework, and performing fine tuning on a support set of the test data set; and performing RUL prediction on the test sets of the fan gear data set and the NASA aero-engine gear data set by using the weights obtained after fine tuning, and outputting a prediction mean value, a variance, a confidence band and a prediction band.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of machine learning, and in particular to a remaining useful life prediction method, system, medium and device based on deep Gaussian processes (DGP) and meta-learning. BACKGROUND

[0002] In the field of predictive maintenance and health management (PHM), accurately predicting the remaining useful life (RUL) of mechanical systems is crucial for improving equipment reliability and reducing maintenance costs. For example, in systems such as aircraft engines and industrial turbines, RUL prediction can help develop preventive maintenance plans to avoid unexpected failures. However, traditional machine learning methods usually require a large amount of labeled data to train the model, while the data of new equipment or new tasks is often limited, making it difficult to meet the training requirements. In addition, traditional methods usually only provide point estimates, lacking uncertainty information in the prediction, which is crucial for risk assessment and decision-making.

[0003] Meta-learning enables models to quickly adapt to new tasks with a small number of samples by "learning how to learn". However, applying meta-learning to RUL prediction faces the following challenges: 1. Sensor data from mechanical systems often has complex nonlinear relationships, and the amount of data is large, increasing the difficulty of modeling. 2. RUL prediction needs to handle time series features while providing probabilistic predictions to quantify uncertainty. 3. Gaussian Processes (GPs) are a powerful probabilistic model that can provide uncertainty estimates, but their computational complexity is high, making it difficult to apply directly to large-scale datasets. Deep Gaussian Processes extend the modeling capabilities through multi-layer structures, but the computational cost is further increased.

[0004] Therefore, there is an urgent need for an efficient method that combines the advantages of meta-learning and deep Gaussian processes, achieving few-shot adaptation, probabilistic prediction, and generalization across datasets to meet the practical needs of RUL prediction. SUMMARY

[0005] To address the limitations in few-shot scenarios and the lack of uncertainty estimates, the present application aims to provide a remaining useful life prediction method, system, medium and device based on deep Gaussian processes and meta-learning, which can quickly adapt to new tasks with a small number of samples and provide prediction results with uncertainty estimates.

[0006] To achieve the above object, in the first aspect, the technical scheme adopted by the application is as follows: a remaining useful life prediction method based on deep Gaussian process and meta-learning, comprising: obtaining original data from a NASA aircraft engine gear dataset, a PHM dataset and a fan gearbox dataset, preprocessing and constructing a multi-task dataset suitable for meta-learning; wherein the PHM dataset contains sensor data and corresponding RUL labels of multiple device units for meta-training; the NASA aircraft engine gear dataset and the fan gearbox dataset contain a small number of support set samples and test set samples for meta-testing; a multi-layer deep Gaussian process model is constructed based on the multi-task dataset, including an input layer, a hidden layer and an output layer; the hidden layer and the output layer both adopt a variational Gaussian process, a radial basis function kernel is used as a covariance function, and a multi-task Gaussian likelihood function is used to model the uncertainty of RUL prediction; meta-training is performed on the PHM dataset by using the deep Gaussian and meta-learning framework, the model is optimized through inner and outer loops, the Adam optimizer is used to learn cross-task generalization, and the generalized weight is obtained; wherein the inner loop performs gradient descent on the support set to update the task-specific parameters; the outer loop calculates the loss on the query set to update the global parameters; the last layer parameters and the likelihood function parameters obtained by meta-training are transferred to the fan gearbox dataset and the NASA aircraft engine dataset based on the same multi-layer deep Gaussian process meta-learning model framework, and the weight fine-tuning is performed on the support set of the test dataset, the Adam optimizer is used to perform multiple gradient updates, so that the multi-layer deep Gaussian process meta-learning model quickly adapts to new tasks; based on the fine-tuned weight, the multi-layer deep Gaussian process meta-learning model is used to predict the RUL of the test set of the fan gearbox dataset and the NASA aircraft engine gear dataset, and the prediction mean, variance, 95% confidence band and 95% prediction band are output, and the model performance is evaluated, and the real RUL and the predicted RUL and their confidence intervals are compared through visualization, wherein the confidence interval is for the predicted RUL.

[0007] Further, the original data is obtained from the NASA aircraft engine gear dataset, the PHM dataset and the fan gearbox dataset, preprocessed and constructed into a multi-task dataset suitable for meta-learning, comprising:

[0008] The input features and RUL labels are normalized to scale their values to the interval [-1, 1];

[0009] The PHM dataset is divided into multiple tasks, each task corresponding to the data of a device unit, task division and batch processing are performed, including a support set and a query set, data preparation is completed and a task format suitable for meta-learning is constructed.

[0010] Further, a multi-layer deep Gaussian process model is constructed based on the multi-task dataset, comprising:

[0011] According to the Gaussian process model, initial modeling is performed through an input feature vector, a feature extraction layer composed of k variational Gaussian process units is introduced, and a remaining service life prediction value is output;

[0012] The latent variable u is modeled through variational inference, and it is assumed that the latent variable u follows a Gaussian distribution with a mean m and a covariance matrix s; the input features are grouped through a K-means clustering algorithm to obtain M cluster centers, which are used to initialize the parameters of the variational distribution;

[0013] Nonlinear mapping of the feature space is realized through a Gaussian radial basis function, and the kernel function k(x,x') is defined as an exponential form with variance and length scale as parameters to measure the similarity between input vectors x and x i ′;

[0014] The multi-task Gaussian process model describes the multi-time series data through a joint probability distribution;

[0015] The framework of Bayesian optimization maximizes the objective function to optimize the model parameters, and the objective function is maximized, which is composed of the weighted sum of the log-likelihood of the prediction distribution and the KL divergence term, and the model construction is completed. The core meta-learning training process will be performed on the source dataset.

[0016] Further, the deep Gaussian and meta-learning framework is used to perform meta-training on the PHM dataset, and the model is optimized through inner and outer loops. The Adam optimizer is used to learn cross-task generalization, and the generalized weights are obtained. The inner loop performs gradient descent on the support set to update the task-specific parameters; the outer loop calculates the loss on the query set to update the global parameters, including:

[0017] The model parameters are optimized through the meta-learning method;

[0018] The task set is divided into a support set and a query set, where the support set is used for model training and the query set is used for performance evaluation. The task data comes from actual industrial scenarios; the model optimizes the parameters on the support set and verifies the prediction performance on the query set;

[0019] The model parameters are optimized by minimizing the support set loss function , and a supervised learning framework for task decomposition is built;

[0020] The deep learning framework based on the Adam optimization algorithm is used to optimize the model parameters through an adaptive momentum estimation method. The parameter update is realized through the Adam algorithm, which combines the normalized form of the momentum m t and the square gradient v t to adjust the parameters θ t under the learning rate η.

[0021] Further, the model parameters are optimized by the meta-learning method, including:

[0022] The initial parameters θ are updated on the support set by gradient descent, and the performance on the query set is taken as the optimization target;

[0023] The updated parameters θ' f The loss is calculated on the query set, and the initial parameters θ are adjusted by gradient descent to minimize the expected loss on the query set;

[0024] In the hyperparameter setting, the learning rates α=0.01 and β=0.001 are used to control the gradient update step size of the support set and the query set respectively, to ensure the stable convergence of the model in the meta-training process; α is the inner loop learning rate, and β is the outer loop learning rate.

[0025] Further, the last layer parameters and the likelihood function parameters obtained by meta-training are transferred to the fan gearbox dataset and the NASA aircraft engine dataset based on the same multi-layer deep Gaussian process meta-learning model framework, and the weight fine-tuning is performed on the support set of the test dataset. The Adam optimizer is used to perform multiple gradient updates, and the multi-layer deep Gaussian process meta-learning model can quickly adapt to new tasks, including:

[0026] By transferring the meta-parameters to the task-specific parameters φ L and φ HM , a fine-tuning optimization framework based on few-shot learning is constructed, and the model parameters are quickly adapted by minimizing the fine-tuning loss function;

[0027] The uncertainty in the task degradation process is described by a time-decaying noise variance, where the initial noise variance decays exponentially with time t.

[0028] Further, based on the fine-tuned weights, the multi-layer deep Gaussian process meta-learning model is used to predict the RUL of the fan gearbox dataset and the NASA aircraft engine gear dataset test set, output the prediction mean, variance, 95% confidence band and 95% prediction band, and evaluate the model performance. By visualizing the comparison between the true RUL and the predicted RUL and their confidence intervals, including:

[0029] The mean function and the variance function are used to realize the probability prediction of unknown input x * , and the prediction framework of the Gaussian process is determined;

[0030] The mean square error is used to quantify the average deviation between the model prediction value and the true value, reflecting the overall fitting ability of the model, and evaluating the performance of the regression task;

[0031] Wherein, the prediction framework of the Gaussian process includes:

[0032] Predicted variance By subtracting the posterior adjustment term calculated from the autocovariance k(x * ,x * ), the uncertainty of the prediction is reflected;

[0033] Based on the dynamic noise modeling meta-learning framework, the robustness of the model in the degradation prediction task is optimized through the parameterized representation of the time dynamic noise variance .

[0034] Assuming that the mean and standard deviation are normally distributed, the confidence interval is constructed at a 95% confidence level; the 95% prediction interval considers the joint influence of variance and .

[0035] In a second aspect, the technical solution adopted by the present application is: a remaining useful life prediction system based on deep Gaussian process and meta-learning, comprising: a multi-task data set construction module, which obtains original data from NASA aircraft engine gear data set, PHM data set and fan gear box data set, performs preprocessing and constructs a multi-task data set suitable for meta-learning; wherein the PHM data set contains sensor data and corresponding RUL labels of multiple device units for meta-training; the NASA aircraft engine gear data set and the fan gear box data set contain a small number of support set samples and test set samples for meta-testing; a model construction module, which constructs a multi-layer deep Gaussian process model based on the multi-task data set, including an input layer, a hidden layer and an output layer; the hidden layer and the output layer both adopt a variational Gaussian process, with a radial basis function kernel as the covariance function, and a multi-task Gaussian likelihood function for modeling the uncertainty of RUL prediction; a meta-training module, which performs meta-training on the PHM data set using the deep Gaussian and meta-learning framework, optimizes the model through inner and outer loops, learns cross-task generalization using the Adam optimizer, and obtains the generalized weights; a model optimization module, which transfers the last layer parameters and the likelihood function parameters obtained by meta-training to the fan gear box data set and the NASA aircraft engine data set based on the same multi-layer deep Gaussian process meta-learning model framework, and fine-tunes the weights on the support set of the test data set, performs multiple gradient updates using the Adam optimizer, so that the multi-layer deep Gaussian process meta-learning model can quickly adapt to new tasks; a meta-prediction module, which performs RUL prediction on the test set of the fan gear box data set and the NASA aircraft engine gear data set based on the fine-tuned weights using the multi-layer deep Gaussian process meta-learning model, outputs the predicted mean, variance, 95% confidence band and 95% prediction band, and evaluates the model performance, and compares the real RUL and the predicted RUL, as well as the confidence interval of the real RUL and the predicted RUL through visualization.

[0036] In a third aspect, the present application takes the technical solution of: a computer readable storage medium storing one or more programs, the one or more programs comprising instructions which, when executed by a computing device, cause the computing device to perform any of the above methods.

[0037] In a fourth aspect, the present application takes the technical solution of: a computing device comprising: one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs comprise instructions for performing any of the above methods.

[0038] The present application has the following advantages due to the above technical solutions:

[0039] In the meta-training phase, a meta-learning algorithm is used to train on the source dataset to learn the initialization parameters θ that are universal across tasks; in the cross-dataset parameter transfer phase, θ is transferred to the new model of the target dataset, and the distribution alignment module is used to compensate for the differences between datasets; in the small sample fine-tuning phase, the model is fine-tuned using the support set (≤30 samples) of the target dataset, and the adaptive efficiency of the variational inference optimized deep Gaussian process is used; in the prediction and uncertainty quantification phase, the RUL prediction is performed based on the fine-tuned variational deep Gaussian process, the task-adaptive structured inductive point system is used to reduce the computational complexity, and the confidence band-prediction band double evaluation system is constructed to verify the effectiveness of the model parameters through statistical interval and define the prediction fluctuation range, thereby enhancing the quantification representation ability of the randomness of the degradation process. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 is the overall flowchart of the residual useful life prediction method based on deep Gaussian process and meta-learning in the embodiments of the present application, which shows the complete process from data preparation to final evaluation, including the following key steps: data preparation, meta-training, parameter transfer, fine-tuning, prediction and evaluation;

[0041] Figure 2 is the hierarchical structure diagram of the deep Gaussian process model in the embodiments of the present application, which shows the connection relationship of the input layer, the hidden Gaussian process layer and the output Gaussian process layer of the model, and the flow path of data from input to output;

[0042] Figure 3 is a schematic diagram of the meta-learning training method in the embodiments of the present application, which shows the detailed visual representation of the meta-training and meta-testing processes, and highlights the key components such as parameter update, inner loop and outer loop mechanism. DETAILED DESCRIPTION

[0043] In order to realize few-sample adaptation, probabilistic prediction and generalization ability across datasets to meet the actual needs of RUL prediction, the application provides a remaining useful life prediction method, system, medium and equipment based on deep Gaussian process and meta-learning, which comprises the following steps: meta-training on a source dataset (such as a PHM dataset) to learn general model parameters; transferring the model parameters obtained by meta-training to a new model of a target dataset (such as a fan gear box dataset and a NASA aircraft engine dataset); fine-tuning the model using a small number of samples (support set) of the target dataset to adapt to the specific characteristics of the new task; finally, using the fine-tuned model to predict the RUL of the test set, while providing uncertainty estimation such as 95% confidence interval.

[0044] To make the objectives, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions of the embodiments of the present application will be described clearly and completely below with reference to the drawings of the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the described embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art belong to the scope of protection of the present application.

[0045] It should be noted that the terms used herein are only intended to describe specific embodiments, and are not intended to limit the exemplary embodiments according to the present application. As used herein, the singular form is intended to include the plural form unless the context clearly indicates otherwise, and furthermore, it should be understood that when the terms "comprise" and / or "include" are used in the specification, there is a feature, step, operation, device, component and / or combination thereof.

[0046] In one embodiment of the present application, a remaining useful life prediction method based on deep Gaussian process and meta-learning is provided, in particular a remaining useful life (RUL) prediction method for predictive maintenance and health management (PHM), based on deep Gaussian process (DGP) and model-agnostic meta-learning (MAML), for quickly adapting to new tasks with few samples and providing RUL prediction with uncertainty estimation, suitable for mechanical system maintenance in the fields of aviation, industrial equipment, etc. In this embodiment, as shown in the figure, the method comprises the following steps: Figure 1

[0047] ​1) Obtain raw data from the NASA aero-engine gear dataset, PHM dataset, and wind turbine gearbox dataset, preprocess them, and construct a multi-task dataset suitable for meta-learning; the PHM dataset contains sensor data (such as vibration and temperature) and corresponding RUL labels for multiple device units for meta-training; the NASA aero-engine gear dataset and wind turbine gearbox dataset contain a small number of support set samples (for fine-tuning) and test set samples (for evaluation) for meta-testing respectively.

[0048] 2) A multi-layer deep Gaussian process model is constructed based on a multi-task dataset, including an input layer, a hidden layer, and an output layer. Both the hidden layer and the output layer adopt variational Gaussian processes, with radial basis function kernels as covariance functions, and multi-task Gaussian likelihood functions are used to model the uncertainty of RUL prediction.

[0049] 3) Meta-training is performed on the PHM dataset using a deep Gaussian and meta-learning framework. The model is optimized through inner and outer loops, and the Adam optimizer is used to learn cross-task generalization to obtain the generalized weights. The inner loop performs gradient descent on the support set to update task-specific parameters, while the outer loop calculates the loss on the query set, updates global parameters, and uses the Adam optimizer for optimization.

[0050] 4) The parameters of the last layer and the likelihood function obtained from the meta-training are transferred to the wind turbine gearbox dataset and the NASA aero-engine dataset based on the same multi-layer deep Gaussian process meta-learning model framework. The weights are fine-tuned on the support set of the test dataset. The Adam optimizer is used to perform multiple gradient updates so that the multi-layer deep Gaussian process meta-learning model can quickly adapt to new tasks.

[0051] 5) Based on the fine-tuned weights, a multi-layer deep Gaussian process meta-learning model is used to predict the RUL of the wind turbine gearbox dataset and the NASA aero-engine gear dataset. The model outputs the predicted mean, variance, 95% confidence band and 95% prediction band, and evaluates the model performance by visually comparing the true RUL with the predicted RUL, and comparing the confidence intervals of the true RUL with the predicted RUL. The confidence interval is for the predicted RUL.

[0052] In step 1) above, data preparation is a fundamental step in RUL prediction, which aims to load raw data, preprocess it, and construct a multi-task dataset suitable for meta-learning.

[0053] In this embodiment, the PHM dataset (PHM2012 challenge dataset) provides bearing lifecycle degradation data, supporting the development and verification of algorithms for predicting the remaining useful life (RUL) of mechanical equipment. Accelerated degradation experiments simulate bearing failure, covering the entire process from normal operation to complete failure, addressing system safety, availability, and maintenance cost issues caused by bearing failures in industrial scenarios.

[0054] The data acquisition system consists of three parts. The rotation system is driven by a 250W asynchronous motor, with the speed controlled within ≤2000rpm and torque transmitted via a gearbox. The load system applies a radial load (maximum 4000N) via a pneumatic-hydraulic cylinder, combined with a lever amplification mechanism to accelerate the degradation of the tested bearing. The monitoring system includes: vibration signal acquisition: two orthogonally mounted accelerometers (range ±50g, sampling frequency 25.6kHz), radially fixed to the outer ring of the bearing; and temperature signal acquisition: a platinum resistance PT100 sensor (sampling frequency 10Hz) embedded near the outer ring of the bearing. Operating parameters are recorded synchronously: speed, load force, and torque parameters are monitored in real time at a sampling frequency of 100Hz, as shown in Table 1.

[0055] Table 1 Experimental Conditions

[0056]

[0057] Bearing failure is defined as a vibration amplitude exceeding 20g, marking the end of the actual remaining service life. The degradation mode is a natural composite degradation caused by multiple types of defects, including rolling elements, inner and outer rings, and cages, eliminating the possibility of artificially pre-inducing single faults.

[0058] The experimental configuration of the data acquisition system is as follows: Vibration data is sampled at a frequency of 25.6 kHz, using a dual-channel synchronous acquisition system to measure horizontal and vertical axial acceleration. Acquisition is triggered every 10 seconds, lasting 0.1 seconds each time, resulting in 2560 samples. Temperature data is sampled at a frequency of 10 Hz using a PT100 platinum resistance thermometer conforming to IEC 751 standards. Acquisition is triggered every minute, lasting 60 seconds each time, resulting in 600 samples. Data is stored in ASCII text format, with vibration and temperature data saved in separate files. Each line of record includes a timestamp and the corresponding sensor reading. Specific data information and dataset division are shown in Table 2.

[0059] Table 2 Dataset Partitioning

[0060]

[0061] In this embodiment, a planetary gearbox test bench for wind turbines is built to conduct accelerated life tests on planetary gears, thereby constructing a wind turbine gearbox dataset. The experimental system consists of the following components: a planetary gearbox, a drive motor, a braking device and its control unit, and a data acquisition system (including acceleration sensors, eddy current sensors, etc.). The planetary gearbox used in the experiment is a three-stage structure with a speed ratio of 1 / 77.

[0062] To improve experimental efficiency and reduce costs, two methods were employed to accelerate fatigue life testing without affecting the wear failure mechanism. First, a suitable load was applied using a brake to accelerate the aging process. Second, one planetary gear in the third-stage gear train was replaced with a gear that had not undergone surface heat treatment, thereby reducing its surface hardness and making it more susceptible to wear. In the experiment, the sampling frequency was set to 20480 Hz, with a single sampling duration of 10 seconds and a sampling interval of 10 minutes, for a total duration of 9300 minutes. The training set comprised 80% of the experimental data, and the test set comprised 20%.

[0063] In this embodiment, the NASA C-MAPSS Prediction and Health Management dataset for aero-engines contains full-cycle failure simulation data for turbofan jet engines. This dataset covers four subsets (FD001-FD004), whose multivariate time-series data characterize the engine degradation process under different operating conditions and failure modes. Each time series corresponds to an independent engine and includes user-unknown initial wear variability, three operating parameters affecting performance, and sensor noise. Data columns include unit number, operating cycle, three operating parameters, and 26 sensor measurements. The training subset contains the complete degradation trajectory up to system failure, while the test subset terminates before failure. The core objective is to predict the remaining useful life (RUL), defined as the number of operating cycles from the last data point to failure. The dataset specifications are shown in Table 3.

[0064] Table 3 NASA Aircraft Engine Gear Dataset

[0065]

[0066]

[0067] In this embodiment, raw data is obtained from the NASA aero-engine gear dataset, the PHM dataset, and the wind turbine gearbox dataset, preprocessed, and a multi-task dataset suitable for meta-learning is constructed, including the following steps:

[0068] 1.1) Normalize the input features and RUL labels to scale their values ​​to the range of [-1,1] to eliminate dimensional differences and improve model training stability;

[0069] The normalization formula is as follows:

[0070]

[0071] Where x is the original feature value, x min and x max Let be the minimum and maximum values ​​of the feature, respectively, and y be the original RUL value. min and y max These are the minimum and maximum values ​​of RUL, respectively, 10 -8 To avoid dividing small positive numbers by zero.

[0072] 1.2) Divide the PHM dataset into multiple tasks, each task corresponding to the data of one device unit. Perform task partitioning and batch processing, including a support set (for model adaptation) and a query set (for evaluation), complete data preparation, and construct a task format suitable for meta-learning.

[0073] The batch data format is as follows:

[0074]

[0075] In the formula, support is the support set, query is the query set, and M is the number of tasks in the batch.

[0076] In step 2) above, if Figure 2 As shown, the construction of a multi-layer deep Gaussian process model based on a multi-task dataset includes the following steps:

[0077] 2.1) Based on the Gaussian process model, by inputting the feature vector x∈R d Initial modeling is performed, where x represents the input feature vector and d is the feature dimension. A feature extraction layer consisting of k variational Gaussian process units is introduced, and the remaining useful life prediction value is output; where k represents the number of variational Gaussian process units, and the output function uses Gaussian process prediction.

[0078] Specifically, this is achieved through the remaining useful life prediction formula:

[0079] h1=h2=f(x)~GP(μ1(x),k1(x,x'))

[0080] In the formula, h1 and h2 represent the hidden layer outputs of the first and second layers, f(x) is the Gaussian process function of the first layer, and GP(μ1(x),k1(x,x')) represents the Gaussian process defined by the mean function μ1(x) and the covariance function k1(x,x'), where x′ is another instance of the input sample.

[0081] y=f(h)~GP(μ2(h),k2(h,h'))

[0082] In the formula, y represents the final predicted output, f(h) is the Gaussian process function of the second layer, and GP(μ2(h),k2(h,h')) represents the Gaussian process defined by the mean function μ2(h) and the covariance function k2(h,h'), where h' is another instance of the hidden layer output.

[0083] 2.2) Model the latent variable u through variational inference, assuming that the latent variable u follows a Gaussian distribution with mean m and covariance matrix s; group the input features using the K-means clustering algorithm to obtain M cluster centers, which are used to initialize the parameters of the variational distribution; in order to predict the remaining service life of the bearing.

[0084] The variational distribution is as follows:

[0085] q(u)=N(m,s)

[0086] In the formula, q(u) represents the variational distribution, N represents the Gaussian distribution, m is the mean vector, and s is the covariance matrix. Next, the value of u is calculated using the Cholesky decomposition method, and an optimization objective is constructed based on the training data and the corresponding labels.

[0087] The input features are grouped using the K-means clustering algorithm to obtain M cluster centers, which are used to initialize the parameters of the variational distribution.

[0088]

[0089] In the formula, K-means represents the K-means clustering algorithm. The input feature set is M, where M is the number of clusters (M = 256 in this experiment), d is the feature dimension, and R is the number of clusters. M×D Represents the matrix space.

[0090] 2.3) Nonlinear mapping of the feature space is achieved through Gaussian radial basis functions. The kernel function k(x,x′) is defined as an exponential form with variance and length scale as parameters to measure the relationship between the input vector x and x′. i Similarity between ';

[0091]

[0092] In the formula, σ 2 To output variance, control the magnitude of the kernel function, x i and x i '' represents the i-th component of the input vector, d is the dimension of the input vector, and l is the length scale, which adjusts the speed of similarity decay.

[0093] 2.4) The multi-task Gaussian process model describes multi-time series data through a joint probability distribution;

[0094] Specifically, let's assume the observed value y t It follows the mean function f t and variance The Gaussian distribution with parameter is used, and the joint probability density is expressed as an independent product of time steps t from 1 to T:

[0095]

[0096] In the formula, p(y|f) represents the joint probability density of the observed values ​​y under a given function f. Let y be a normal distribution at time step t. t For the observed value, f t It is a mean function. To observe the noise variance, T represents the total number of time steps. Hyperparameter optimization is constrained by a specified range. Simultaneously, it is assumed that the degradation process of each independent task is modeled by a single independent prediction task, with the constraint T = 1.

[0097] The variance decomposition formula is used to represent the observed variance V[y]. t The composition of ] includes the mean function variance V[f t and noise variance The sum of:

[0098]

[0099] In the formula, V[y t ] represents the total variance of observations at time step t, V[f t ] is the mean function f t variance To add noise variance, y t These are predicted values.

[0100] 2.5) The Bayesian optimization framework maximizes the objective function. To optimize model parameters and maximize the objective function. The model is constructed by a weighted sum of the log-likelihood of the predicted distribution and the KL divergence term. The core meta-learning training process is carried out on the source dataset, with the aim of learning initialization parameters that can quickly adapt to new tasks.

[0101] Where, maximizing the objective function for:

[0102]

[0103] In the formula, Let y be the expected log-likelihood of the i-th sample. i For the observed value, f iLet KL[q(u)||p(u) be the prediction function, representing the KL divergence between the variational distribution q(u) and the prior distribution p(u), and N be the total number of samples.

[0104] In step 3) above, if Figure 3 As shown, meta-training is performed on the PHM dataset using a deep Gaussian and meta-learning framework. The model is optimized through inner and outer loops, and the Adam optimizer is used to learn cross-task generalization to obtain the generalized weights. The inner loop performs gradient descent on the support set to update task-specific parameters. The outer loop calculates the loss on the query set and updates the global parameters, including the following steps:

[0105] 3.1) Optimize model parameters through meta-learning methods to achieve the ability to quickly adapt to new tasks:

[0106] 3.1.1) The initial parameters θ are updated on the support set using gradient descent, and the performance on the query set is used as the optimization objective;

[0107]

[0108] In the formula, θ′ f This represents the updated parameters, where θ is the initial parameter and α is the learning rate. To support set loss function The gradient of f with respect to θ θ This is a model parameterized by parameter θ.

[0109] 3.1.2) Updated parameter θ′ f The loss is computed on the query set, and the initial parameter θ is adjusted by gradient descent to minimize the expected loss on the query set.

[0110]

[0111] In the formula, θ represents the updated meta-model parameters, and β is the meta-learning rate. Loss of query set With respect to the gradient of θ, T i ~p(T) represents the task sampled from the task distribution p(T). This is the updated model.

[0112] 3.1.3) In the hyperparameter settings, the learning rates α = 0.01 and β = 0.001 are used to control the gradient update step size of the support set and query set, respectively, to ensure the stable convergence of the model during the meta-training process; α is the inner loop learning rate and β is the outer loop learning rate.

[0113] Through the above optimization strategies, the meta-learning framework achieves rapid adaptation to new tasks. By combining the dual optimization of support set and query set, it effectively improves the generalization performance and meta-learning efficiency of the model.

[0114] 3.2) The task set is divided into a support set and a query set. The support set is used for model training, and the query set is used for performance evaluation. The task data comes from real industrial scenarios. The model is optimized on the support set and its prediction performance is verified on the query set.

[0115]

[0116] In the formula, Denotes the support set for task i, (x s ,y s Let x be the s-th sample pair. s For the input features, y s For the corresponding label, s ranges from 1 to 20, representing the number of samples in the support set.

[0117]

[0118] In the formula, Describes the query set for task i, (x q ,y q Let x be the q-th sample pair. q For the input features, y q For the corresponding labels, q ranges from 21 to 40, representing the number of samples in the query set. Through the above task partitioning, the model optimizes its parameters on the support set and validates its prediction performance on the query set, ensuring the independence of training and testing data, and making it suitable for RUL prediction in dynamic degradation processes.

[0119] 3.3) By minimizing the support set loss function To optimize model parameters and build a supervised learning framework for task decomposition;

[0120] The loss function measures the deviation between the predicted value and the true value in the form of mean squared error, and the data comes from the support set.

[0121]

[0122] In the formula, This means minimizing the support set loss for parameter θ. To support the number of samples in the set, (x,y) supports input-output pairs in the set, where x is the input feature, y is the true label, and μ(x;θ) is the model prediction.

[0123] Model initialization is achieved through cloning. A copy is first created from the base learner to ensure independent training for each task, avoiding parameter interference. During training, the cloned learner updates its parameters based on the support set data. The optimized model is then used for subsequent query set evaluation, ensuring improved task adaptability.

[0124] 3.4) A deep learning framework based on the Adam optimization algorithm is adopted. The model parameters are optimized through an adaptive momentum estimation method. Parameter updates are implemented using the Adam algorithm, combined with momentum m. t Sum of squared gradients v t The normalized form, adjusting the parameter θ under the learning rate η. t .

[0125]

[0126] In the formula, θ t+1 This represents the updated parameter, θ. t Here, η is the current parameter, and η is the learning rate. The first-order momentum is used to correct for the deviation. The second-order momentum is the correction for the deviation. This is a numerical stability term.

[0127] After obtaining generalizable initialization parameters through meta-training, the key advantage of this invention lies in its ability to efficiently transfer this knowledge to new target devices or datasets (such as wind turbine gearboxes and NASA aero-engine datasets) and adapt quickly with a small number of samples.

[0128] In step 4) above, the parameters of the last layer and the likelihood function parameters obtained from the meta-training are transferred to the wind turbine gearbox dataset and the NASA aero-engine dataset, which are based on the same multi-layer deep Gaussian process meta-learning model framework. Weight fine-tuning is then performed on the support set of the test dataset, and multiple gradient updates are executed using the Adam optimizer. The multi-layer deep Gaussian process meta-learning model can quickly adapt to new tasks, including the following steps:

[0129] 4.1) By migrating the meta-parameters to the task-specific parameter φ L and φ HM This approach combines several methods to improve the model's adaptability to few-shot tasks. The few-shot learning-based fine-tuning optimization framework achieves rapid adaptation of model parameters by minimizing the fine-tuning loss function, thus constructing a few-shot learning-based fine-tuning optimization framework.

[0130]

[0131] In the formula, This represents the task-specific parameter for the t-th iteration. φ represents the meta-parameter of the t-th generation. L and φ HM These represent the final task-specific parameters and high-level meta-parameters, respectively.

[0132] The loss function is based on the mean squared error of the support set, and the number of samples K represents the number of support samples in each class, which is currently set to 20.

[0133]

[0134] In the formula, This indicates that the parameter θ NASA Minimize the fine-tuning loss, where K is the number of samples per class in the support set, and y k Let μ(x) be the true label of the k-th sample. k ;θ NASA ) represents the model's predicted value, x k The input features are used. The fine-tuning process uses a few-sample setting, supporting a set of samples K=20, meaning that each task class contains 20 samples, which are used for updating the model's parameters.

[0135] Parameter updates are achieved through gradient descent, with the initial parameters adjusted by combining the gradient of the fine-tuning loss.

[0136]

[0137] In the formula, This represents the parameters for the (t+1)th iteration. Here, η is the current parameter, and η is the learning rate. This is to fine-tune the gradient of the loss with respect to θ.

[0138] 4.2) The uncertainty in the task degradation process is described by the time-decayed noise variance, where the initial noise variance decays exponentially with time t.

[0139]

[0140] In the formula, This represents the noise variance at time t. Let be the initial noise variance, γ be the decay rate, t be the time variable, and exp(-γt) represent the exponential decay term.

[0141] Initial noise The variance is inherited from the high-level meta-model (PHM model) to reflect the uncertainty of the initial state of the task, and the attenuation rate γ controls the rate of noise change over time. A noise attenuation rate of 0.2 indicates that the noise variance exhibits a moderate decreasing trend over time, consistent with the noise characteristics during the degradation process of mechanical systems. Constraints ensure the robustness of the model at different degradation stages. The datasets selected are based on the PHM model, the wind turbine gearbox dataset, and NASA aero-engine data, covering diverse degradation scenarios of industrial mechanical systems.

[0142] After fine-tuning with a small number of samples on the target dataset, the model acquires predictive capabilities for this specific task. The final step is to use the fine-tuned model to perform actual RUL predictions and evaluate the prediction results (including point estimates and uncertainties). Through dynamic noise modeling and dataset transfer, the model achieves improved robustness in cross-domain degradation predictions. Combined with exponential decay and automatic learning mechanisms, it significantly improves prediction accuracy in industrial scenarios.

[0143] In step 5) above, based on the fine-tuned weights, a multi-layer deep Gaussian process meta-learning model is used to predict the RUL (Relative Limiting Parameter) of the wind turbine gearbox dataset and the NASA aero-engine gear dataset. The model outputs the predicted mean, variance, 95% confidence band, and 95% prediction band, and evaluates its performance by visually comparing the actual RUL with the predicted RUL and their confidence intervals. This includes the following steps:

[0144] 5.1) Using the mean function and variance function to achieve the unknown input x * Probabilistic prediction to determine the prediction framework for Gaussian processes;

[0145]

[0146] In the formula, μ(x) * ) represents the input x * The predicted mean, k * Let be the covariance vector between the test points and the training points. Let be the inverse of the covariance matrix of the training points, and m be the weight vector. The kernel function and covariance matrix are defined by a Gaussian process, reflecting prior information about the training data.

[0147] The prediction framework for Gaussian processes includes:

[0148] 5.1.1) Prediction Variance Through the autocovariance k(x) * ,x * The calculation, which subtracts the posterior adjustment term, reflects the uncertainty of the prediction;

[0149]

[0150] In the formula, Let k(x) represent the prediction variance. * ,x * ) represents the autocovariance. This is the posterior covariance adjustment term.

[0151] 5.1.2) A meta-learning framework based on dynamic noise modeling, which analyzes the variance of temporal dynamic noise. The parameterized representation optimizes the robustness of the model in degradation prediction tasks;

[0152]

[0153] In the formula, Let exp(φ) represent the noise variance, be an exponential function, and φ be the logarithmic noise parameter, which is learned through optimization. By parameterizing the noise variance into the form of exp(φ), the model can adaptively adjust the noise level to adapt to the data characteristics at different degradation stages, thereby improving the accuracy and stability of predictions.

[0154] 5.1.3) Assuming the mean and standard deviation are normally distributed, confidence intervals are constructed at a 95% confidence level; the 95% prediction interval takes into account the variance. and The combined effects.

[0155] The confidence interval is:

[0156] [μ-1.96σ m μ+1.96σ m ]

[0157] In the formula, μ represents the predicted mean, and σ m The Z-score represents the mean and standard deviation, with 1.96 being the Z-score at the 95% confidence level.

[0158] The 95% prediction range is:

[0159]

[0160] In the formula, μ represents the predicted mean. The total standard deviation is given, and 1.96 is the Z-score at the 95% confidence level. and These are the mean variance and the noise variance, respectively.

[0161] By modeling the Gaussian process as described above, the model achieves probabilistic prediction of the degradation process. By combining dynamic noise and confidence intervals, the uncertainty is effectively quantified, and the reliability of industrial forecasts is improved.

[0162] 5.2) The mean squared error (MSE) is used to quantify the average deviation between the model's predicted values ​​and the true values, reflecting the overall fitting ability of the model and evaluating the performance of the regression task.

[0163]

[0164] In the formula, MSE represents the mean squared error, N is the total number of samples, and y i μ is the true value of the i-th sample. i This corresponds to the predicted value.

[0165] Furthermore, in order to more intuitively reflect the magnitude of the prediction error, this invention uses the root mean square error (RMSE) as an evaluation index. RMSE is the square root of MSE, and the unit is consistent with the original data.

[0166]

[0167] In the formula, RMSE represents the root mean square error. For mean square error, y i and μ i These represent the actual value and the predicted value, respectively.

[0168] By calculating MSE and RMSE, the model can comprehensively evaluate its predictive performance. MSE provides the average of the squared errors, while RMSE provides an error measure that is relevant to the actual units.

[0169] In summary, this invention addresses two major pain points of traditional methods: weak generalization ability in scenarios with few samples and lack of uncertainty quantification. Through a framework of meta-training-parameter transfer-few-sample fine-tuning, it achieves rapid adaptation and probabilistic prediction across devices and operating conditions.

[0170] In one embodiment of the present invention, a remaining useful life prediction system based on deep Gaussian processes and meta-learning is provided, comprising:

[0171] The multi-task dataset construction module obtains raw data from the NASA aero-engine gear dataset, PHM dataset, and wind turbine gearbox dataset, performs preprocessing, and constructs a multi-task dataset suitable for meta-learning. Among them, the PHM dataset contains sensor data and corresponding RUL labels for multiple device units for meta-training; the NASA aero-engine gear dataset and wind turbine gearbox dataset contain a small number of support set samples and test set samples for meta-testing.

[0172] The model building module constructs a multi-layer deep Gaussian process model based on a multi-task dataset, including an input layer, a hidden layer, and an output layer. Both the hidden layer and the output layer adopt variational Gaussian processes, with radial basis function kernels as covariance functions, and multi-task Gaussian likelihood functions used to model the uncertainty of RUL prediction.

[0173] The meta-training module utilizes a deep Gaussian and meta-learning framework to perform meta-training on the PHM dataset. It optimizes the model through inner and outer loops, and uses the Adam optimizer to learn cross-task generalization to obtain the generalized weights. Specifically, the inner loop performs gradient descent on the support set to update task-specific parameters, while the outer loop calculates the loss on the query set to update global parameters.

[0174] The model optimization module transfers the last layer parameters and likelihood function parameters obtained from meta-training to the wind turbine gearbox dataset and the NASA aero-engine dataset, which are based on the same multi-layer deep Gaussian process meta-learning model framework. It also performs weight fine-tuning on the support set of the test dataset and uses the Adam optimizer to perform multiple gradient updates, enabling the multi-layer deep Gaussian process meta-learning model to quickly adapt to new tasks.

[0175] The meta-prediction module, based on fine-tuned weights, uses a multi-layer deep Gaussian process meta-learning model to predict the RUL of the wind turbine gearbox dataset and the NASA aero-engine gear dataset. It outputs the predicted mean, variance, 95% confidence band, and 95% prediction band, and evaluates the model performance by visually comparing the true RUL with the predicted RUL and their confidence intervals, where the confidence interval is for the predicted RUL.

[0176] In the above embodiments, raw data are obtained from the NASA aero-engine gear dataset, the PHM dataset, and the wind turbine gearbox dataset, preprocessed, and a multi-task dataset suitable for meta-learning is constructed, including:

[0177] Normalize the input features and RUL labels to scale their values ​​to the range of [-1, 1].

[0178] The PHM dataset is divided into multiple tasks, each corresponding to the data of a device unit. Task partitioning and batch processing are performed, including support sets and query sets, to complete data preparation and construct a task format suitable for meta-learning.

[0179] In the above embodiments, constructing a multi-layer deep Gaussian process model based on a multi-task dataset includes:

[0180] Based on the Gaussian process model, initial modeling is performed by inputting feature vectors, and a feature extraction layer composed of k variational Gaussian process units is introduced to output the predicted value of remaining useful life.

[0181] The latent variable u is modeled by variational inference, assuming that the latent variable u follows a Gaussian distribution with mean m and covariance matrix s; the input features are grouped by the K-means clustering algorithm to obtain M cluster centers, which are used to initialize the parameters of the variational distribution.

[0182] Nonlinear mapping of the feature space is achieved through Gaussian radial basis functions. The kernel function k(x,x′) is defined as an exponential form with variance and length scale as parameters to measure the relationship between the input vector x and x′. i Similarity between ';

[0183] Multi-task Gaussian process models describe multi-time series data through joint probability distributions;

[0184] The framework of Bayesian optimization maximizes the objective function. To optimize model parameters and maximize the objective function. The model is constructed by a weighted sum of the log-likelihood of the predicted distribution and the KL divergence term. The core meta-learning training process will be carried out on the source dataset.

[0185] In the above embodiments, meta-training is performed on the PHM dataset using a deep Gaussian and meta-learning framework. The model is optimized through inner and outer loops, and the Adam optimizer is used to learn cross-task generalization to obtain the generalized weights. The inner loop performs gradient descent on the support set to update task-specific parameters; the outer loop calculates the loss on the query set and updates global parameters, including:

[0186] Optimize model parameters using meta-learning methods;

[0187] The task set is divided into a support set and a query set. The support set is used for model training, and the query set is used for performance evaluation. The task data comes from real industrial scenarios. The model performs parameter optimization on the support set and verifies the prediction performance on the query set.

[0188] By minimizing the support set loss function To optimize model parameters and build a supervised learning framework for task decomposition;

[0189] A deep learning framework based on the Adam optimization algorithm is adopted, and the model parameters are optimized through an adaptive momentum estimation method. Parameter updates are implemented using the Adam algorithm, combined with momentum m. t Sum of squared gradients v t The normalized form, adjusting the parameter θ under the learning rate η. t .

[0190] In the above embodiments, optimizing model parameters through meta-learning methods includes:

[0191] The initial parameter θ is updated on the support set via gradient descent, and the performance on the query set is used as the optimization objective.

[0192] Updated parameter θ′ f The loss is computed on the query set, and the initial parameter θ is adjusted by gradient descent to minimize the expected loss on the query set.

[0193] In the hyperparameter settings, learning rates α = 0.01 and β = 0.001 are used to control the gradient update step size of the support set and query set, respectively, to ensure stable convergence of the model during meta-training; α is the inner loop learning rate, and β is the outer loop learning rate. In the above embodiment, the parameters of the last layer and the likelihood function parameters obtained from meta-training are transferred to the wind turbine gearbox dataset and the NASA aero-engine dataset based on the same multi-layer deep Gaussian process meta-learning model framework, and the weights are fine-tuned on the support set of the test dataset. Multiple gradient updates are performed using the Adam optimizer. The multi-layer deep Gaussian process meta-learning model can quickly adapt to new tasks, including:

[0194] By migrating the meta-parameters to the task-specific parameter φ L and φ HM This approach combines several methods, using a few-shot learning-based fine-tuning optimization framework to achieve rapid adaptation of model parameters by minimizing the fine-tuning loss function, thus constructing a few-shot learning-based fine-tuning optimization framework.

[0195] The uncertainty in the task degradation process is described by the time-decayed noise variance, where the initial noise variance decays exponentially with time t.

[0196] In the above embodiments, based on the fine-tuned weights, a multi-layer deep Gaussian process meta-learning model is used to predict the RUL (Relative Limiting Parameter) of the wind turbine gearbox dataset and the NASA aero-engine gear dataset. The model outputs the predicted mean, variance, 95% confidence band, and 95% prediction band, and evaluates its performance by visually comparing the actual RUL with the predicted RUL and their confidence intervals, including:

[0197] The unknown input x is obtained by using the mean function and variance function. * Probabilistic prediction to determine the prediction framework for Gaussian processes;

[0198] The mean squared error is used to quantify the average deviation between the model's predicted values ​​and the actual values, reflecting the model's overall fitting ability and evaluating the performance of the regression task.

[0199] The prediction framework for Gaussian processes includes:

[0200] Predictive variance Through the autocovariance k(x) * ,x * The calculation, which subtracts the posterior adjustment term, reflects the uncertainty of the prediction;

[0201] A meta-learning framework based on dynamic noise modeling, by analyzing the variance of temporal dynamic noise... The parameterized representation optimizes the robustness of the model in degradation prediction tasks;

[0202] Assuming the mean and standard deviation follow a normal distribution, confidence intervals are constructed at a 95% confidence level; the 95% prediction interval takes into account the variance. and The combined effects.

[0203] The system provided in this embodiment is used to execute the above-described method embodiments. For specific processes and details, please refer to the above embodiments, which will not be repeated here.

[0204] In one embodiment of the present invention, a computing device is provided. This computing device can be a terminal and may include a processor, a communication interface, memory, a display screen, and an input device. The processor, communication interface, and memory communicate with each other via a communication bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and computer programs. When the computer programs are executed by the processor, they implement the methods described in the above embodiments. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The communication interface is used for wired or wireless communication with external terminals. Wireless communication can be achieved through Wi-Fi, a management network, NFC (Near Field Communication), or other technologies. The display screen can be a liquid crystal display (LCD) or an e-ink display. The input device can be a touch layer covering the display screen, or buttons, a trackball, or a touchpad mounted on the casing of the computing device, or an external keyboard, touchpad, or mouse. The processor can call logical instructions stored in the memory.

[0205] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0206] In one embodiment of the present invention, a computer program product is provided, the computer program product including a computer program stored on a non-transitory computer-readable storage medium, the computer program including program instructions, and when the program instructions are executed by a computer, the computer is able to perform the methods provided in the above-described method embodiments.

[0207] In one embodiment of the present invention, a non-transitory computer-readable storage medium is provided, which stores server instructions that cause a computer to perform the methods provided in the above embodiments.

[0208] The computer-readable storage medium provided in the above embodiments has a similar implementation principle and technical effect to the above method embodiments, and will not be described again here.

[0209] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0210] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0211] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0212] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting remaining useful life based on deep Gaussian processes and meta-learning, characterized in that, include: Raw data were obtained from the NASA aero-engine gear dataset, PHM dataset, and wind turbine gearbox dataset. The data were preprocessed and a multi-task dataset suitable for meta-learning was constructed. The PHM dataset contains sensor data and corresponding RUL labels for multiple device units for meta-training. The NASA aero-engine gear dataset and wind turbine gearbox dataset contain a small number of support set samples and test set samples for meta-testing. A multi-layer deep Gaussian process model is constructed based on a multi-task dataset, including an input layer, a hidden layer, and an output layer. Both the hidden layer and the output layer adopt variational Gaussian processes, with radial basis function kernels as covariance functions. The multi-task Gaussian likelihood function is used to model the uncertainty of RUL prediction. Meta-training is performed on the PHM dataset using a deep Gaussian and meta-learning framework. The model is optimized through inner and outer loops, and the Adam optimizer is used to learn cross-task generalization to obtain the generalized weights. Specifically, the inner loop performs gradient descent on the support set to update task-specific parameters, while the outer loop calculates the loss on the query set to update global parameters. The parameters of the last layer and the likelihood function obtained from the meta-training are transferred to the wind turbine gearbox dataset and the NASA aero-engine dataset based on the same multi-layer deep Gaussian process meta-learning model framework. The weights are fine-tuned on the support set of the test dataset. The Adam optimizer is used to perform multiple gradient updates, enabling the multi-layer deep Gaussian process meta-learning model to quickly adapt to new tasks. Based on the fine-tuned weights, a multi-layer deep Gaussian process meta-learning model is used to predict the RUL of the wind turbine gearbox dataset and the NASA aero-engine gear dataset. The model outputs the predicted mean, variance, 95% confidence band and 95% prediction band, and evaluates the model performance by visually comparing the true RUL with the predicted RUL and their confidence intervals, where the confidence interval is for the predicted RUL.

2. The remaining lifetime prediction method based on deep Gaussian processes and meta-learning as described in claim 1, characterized in that, Raw data were obtained from the NASA aero-engine gear dataset, the PHM dataset, and the wind turbine gearbox dataset. These datasets were preprocessed and used to construct a multi-task dataset suitable for meta-learning, including: Normalize the input features and RUL labels to scale their values ​​to the range of [-1, 1]. The PHM dataset is divided into multiple tasks, each corresponding to the data of a device unit. Task partitioning and batch processing are performed, including support sets and query sets, to complete data preparation and construct a task format suitable for meta-learning.

3. The remaining lifetime prediction method based on deep Gaussian processes and meta-learning as described in claim 1, characterized in that, A multi-layer deep Gaussian process model is constructed based on a multi-task dataset, including: Based on the Gaussian process model, initial modeling is performed by inputting feature vectors, and a feature extraction layer composed of k variational Gaussian process units is introduced to output the predicted value of remaining useful life. The latent variable u is modeled by variational inference, assuming that the latent variable u follows a Gaussian distribution with mean m and covariance matrix s; the input features are grouped by the K-means clustering algorithm to obtain M cluster centers, which are used to initialize the parameters of the variational distribution. Nonlinear mapping of the feature space is achieved through Gaussian radial basis functions. The kernel function k(x,x′) is defined as an exponential form with variance and length scale as parameters to measure the relationship between the input vector x and x′. i Similarity between '; Multi-task Gaussian process models describe multi-time series data through joint probability distributions; The framework of Bayesian optimization maximizes the objective function. To optimize model parameters and maximize the objective function. The model is constructed by a weighted sum of the log-likelihood of the predicted distribution and the KL divergence term. The core meta-learning training process will be carried out on the source dataset.

4. The remaining lifetime prediction method based on deep Gaussian processes and meta-learning as described in claim 1, characterized in that, Meta-training is performed on the PHM dataset using a deep Gaussian and meta-learning framework. The model is optimized through inner and outer loops. The Adam optimizer is used to learn cross-task generalization and obtain the generalized weights. The inner loop performs gradient descent on the support set to update task-specific parameters. The outer loop calculates the loss on the query set and updates the global parameters, including: Optimize model parameters using meta-learning methods; The task set is divided into a support set and a query set. The support set is used for model training, and the query set is used for performance evaluation. The task data comes from real industrial scenarios. The model performs parameter optimization on the support set and verifies the prediction performance on the query set. By minimizing the support set loss function To optimize model parameters and build a supervised learning framework for task decomposition; A deep learning framework based on the Adam optimization algorithm is adopted, and the model parameters are optimized through an adaptive momentum estimation method. Parameter updates are implemented using the Adam algorithm, combined with momentum m. t Sum of squared gradients v t The normalized form, adjusting the parameter θ under the learning rate η. t .

5. The remaining useful life prediction method based on deep Gaussian processes and meta-learning as described in claim 4, characterized in that, Optimizing model parameters through meta-learning methods includes: The initial parameter θ is updated on the support set via gradient descent, and the performance on the query set is used as the optimization objective. Updated parameter θ′ f The loss is computed on the query set, and the initial parameter θ is adjusted by gradient descent to minimize the expected loss on the query set. In the hyperparameter settings, the learning rates α = 0.01 and β = 0.001 are used to control the gradient update step size of the support set and query set, respectively, to ensure the stable convergence of the model during the meta-training process; α is the inner loop learning rate and β is the outer loop learning rate.

6. The remaining lifetime prediction method based on deep Gaussian processes and meta-learning as described in claim 1, characterized in that, The parameters of the last layer and the likelihood function obtained from the meta-training are transferred to the wind turbine gearbox dataset and the NASA aero-engine dataset, both based on the same multi-layer deep Gaussian process meta-learning model framework. Weight fine-tuning is performed on the support set of the test dataset, and multiple gradient updates are executed using the Adam optimizer. The multi-layer deep Gaussian process meta-learning model can quickly adapt to new tasks, including: By migrating the meta-parameters to the task-specific parameter φ L and φ HM This approach combines several methods, using a few-shot learning-based fine-tuning optimization framework to achieve rapid adaptation of model parameters by minimizing the fine-tuning loss function, thus constructing a few-shot learning-based fine-tuning optimization framework. The uncertainty in the task degradation process is described by the time-decayed noise variance, where the initial noise variance decays exponentially with time t.

7. The remaining lifetime prediction method based on deep Gaussian processes and meta-learning as described in claim 1, characterized in that, Based on the fine-tuned weights, a multi-layer deep Gaussian process meta-learning model is used to predict the relative safety (RUL) of the wind turbine gearbox dataset and the NASA aero-engine gear dataset on the test sets. The model outputs the predicted mean, variance, 95% confidence band, and 95% prediction band. Model performance is evaluated by visually comparing the true RUL with the predicted RUL and their confidence intervals, including: The unknown input x is obtained by using the mean function and variance function. * Probabilistic prediction to determine the prediction framework for Gaussian processes; The mean squared error is used to quantify the average deviation between the model's predicted values ​​and the actual values, reflecting the model's overall fitting ability and evaluating the performance of the regression task. The prediction framework for Gaussian processes includes: Predictive variance Through the autocovariance k(x) * ,x * The calculation, which subtracts the posterior adjustment term, reflects the uncertainty of the prediction; A meta-learning framework based on dynamic noise modeling, by analyzing the variance of temporal dynamic noise... The parameterized representation optimizes the robustness of the model in degradation prediction tasks; Assuming the mean and standard deviation follow a normal distribution, confidence intervals are constructed at a 95% confidence level; the 95% prediction interval takes into account the variance. and The combined effects.

8. A remaining useful life prediction system based on deep Gaussian processes and meta-learning, characterized in that, include: The multi-task dataset construction module obtains raw data from the NASA aero-engine gear dataset, PHM dataset, and wind turbine gearbox dataset, performs preprocessing, and constructs a multi-task dataset suitable for meta-learning. Among them, the PHM dataset contains sensor data and corresponding RUL labels for multiple device units for meta-training; the NASA aero-engine gear dataset and wind turbine gearbox dataset contain a small number of support set samples and test set samples for meta-testing. The model building module constructs a multi-layer deep Gaussian process model based on a multi-task dataset, including an input layer, a hidden layer, and an output layer. Both the hidden layer and the output layer adopt variational Gaussian processes, with radial basis function kernels as covariance functions, and multi-task Gaussian likelihood functions used to model the uncertainty of RUL prediction. The meta-training module utilizes a deep Gaussian and meta-learning framework to perform meta-training on the PHM dataset. It optimizes the model through inner and outer loops, and uses the Adam optimizer to learn cross-task generalization to obtain the generalized weights. The model optimization module transfers the last layer parameters and likelihood function parameters obtained from meta-training to the wind turbine gearbox dataset and NASA aero-engine dataset based on the same multi-layer deep Gaussian process meta-learning model framework, and performs weight fine-tuning on the support set of the test dataset. The Adam optimizer is used to perform multiple gradient updates, enabling the multi-layer deep Gaussian process meta-learning model to quickly adapt to new tasks. The meta-prediction module, based on fine-tuned weights, uses a multi-layer deep Gaussian process meta-learning model to predict the RUL of the wind turbine gearbox dataset and the NASA aero-engine gear dataset. It outputs the predicted mean, variance, 95% confidence band, and 95% prediction band, and evaluates the model performance by visually comparing the true RUL with the predicted RUL, as well as comparing the confidence intervals of the true RUL and the predicted RUL.

9. A computer-readable storage medium for storing one or more programs, characterized in that, The one or more programs include instructions that, when executed by a computing device, cause the computing device to perform any of the methods described in claims 1 to 7.

10. A computing device, characterized in that, include: One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs including instructions for performing any of the methods described in claims 1 to 7.

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