A method and system for predicting the remaining life of a metal bellows
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
- Filing Date
- 2026-02-10
- Publication Date
- 2026-06-16
Smart Images
Figure CN122221207A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of industrial internet and fault prediction health management (PHM) technology, specifically to a method and system for predicting the remaining useful life (RUL) of pipe metal bellows components and the like under varying operating conditions. Background Technology
[0002] Metal bellows, as key flexible connectors in aerospace propulsion systems, petrochemical pipelines, and heating networks, often operate in complex fluid-structure interaction (FSI) environments. Fluid pulsation-induced vibrations can cause fatigue cracks in bellows, ultimately leading to failure. Therefore, accurate prediction of their remaining life is crucial for ensuring equipment safety.
[0003] While existing deep learning-based data-driven methods excel in feature extraction, they still face three major challenges in practical applications:
[0004] Data distribution shift caused by varying operating conditions: In actual engineering, operating parameters such as flow velocity and pressure fluctuate frequently, leading to significant changes in the statistical distribution of monitoring data. Models trained based on specific operating conditions experience a sharp decline in performance under unknown operating conditions.
[0005] Lack of physical interpretability and consistency: Purely data-driven models often operate as "black boxes," easily fitting noise in the data rather than causal mechanisms. In small sample or high-noise environments, predicted degradation trajectories (such as stiffness changes) often exhibit non-monotonic fluctuations that violate physical common sense (e.g., sudden increases in stiffness), leading to unreliable prediction results.
[0006] Computational constraints of edge deployment: Existing high-performance transfer learning models typically rely on workstations or cloud servers, which involve large amounts of computation and high latency, making them difficult to deploy on resource-constrained industrial edge nodes (such as pipeline monitoring terminals) and unable to meet the requirements for millisecond-level real-time response.
[0007] Therefore, there is an urgent need for a remaining lifetime prediction method and system that can integrate physical mechanisms to ensure prediction consistency, adapt to varying operating conditions, and be easy to deploy in a lightweight manner at the edge. Summary of the Invention
[0008] The purpose of this invention is to provide a remaining lifetime prediction method and system (named PCADA-DED) based on physical constraint adversarial domain adaptation and dual ellipsoidal data description, in order to solve the above-mentioned technical problems.
[0009] The technical solution adopted in this invention is as follows:
[0010] This invention provides a method for predicting the remaining life of metal bellows based on Physically Constrained Adversarial Domain Adaptation and Double Ellipsoid Data Description (PCADA-DED). (Refer to...)Figure 1 The method specifically includes the following core steps:
[0011] 1. Obtain source and target domain datasets
[0012] 1.1 Degradation test system in operation of metal bellows (see Figure 5 Using a triaxial accelerometer installed at the corrugations of a metal bellows, the triaxial vibration acceleration signal generated by the flow of the medium in the pipe at time t is collected. .
[0013] 1.2 Data Collection Source domain datasets divided into those with full-lifetime labels (Corresponding to the experimental conditions) and unlabeled target domain dataset (Corresponding to the current operating condition). Figure 1 (The data refers to "source domain data" and "target domain data"). N represents the number of samples.
[0014] 2. Extracting high-dimensional features
[0015] 2.1 Constructing a Feature Extractor It is used to extract potential high-dimensional features from data.
[0016] 2.2 For the vibration acceleration signal input at any time during step 1 via feature extractor After mapping, a high-dimensional input feature vector is obtained. .
[0017]
[0018] 3. Calculate the loss function for the anti-process.
[0019] 3.1 Constructing the discriminator The main purpose is to complement the feature extractor constructed in step 2.1. Establish a minimax game. Domain discriminator. Identify the high-dimensional input features obtained in step 2.2 Ultimately, it originates from the source domain defined in step 1.2. or target domain feature extractor It then attempts to generate domain-invariant features that can confuse the discriminator.
[0020] 3.2 Signals acquired in step 1 (Divided into source domain datasets) and target domain dataset Using this as input, calculate the loss function for the adversarial process. :
[0021]
[0022] in, This represents the expected operation on the distribution of data in the source domain. This represents the expected operation on the distribution of data in the target domain.
[0023] 3.3 Fix the whole Branch, only maximize renew This is to enhance its ability to distinguish differences in operating conditions.
[0024] 4. Calculate the total physical constraint loss function. (Reference Figure 2 )
[0025] 4.1 The acceleration signal acquired in step 1.1 is integrated using a numerical integration method. Decomposed into system state vectors , which correspond to the system's acceleration, velocity, and displacement, respectively.
[0026] 4.2 Constructing the Physical Regression Branch The high-dimensional input feature vector from step 2.2 As input, calculate the stiffness estimate. :
[0027]
[0028] in, and Learnable parameters for the regression branch; Softplus activation function ( ) is used to apply a constant positive stiffness ( Physical constraints.
[0029] 4.3 From the system state vector in step 4.1 As input, calculate the dynamic loss. :
[0030]
[0031] in, For the equivalent mass of the bellows, The damping coefficient is... It is a bounded variable controlled by operating parameters and is related to the excitation force generated by the fluid. It is a bounded variable controlled by operating parameters and is related to the excitation force generated by the fluid.
[0032] By minimizing the residual between the network's predicted state and the physical equations, the backpropagation of the gradient will force the feature extractor to... Adjust the weights to make the generated features It implicitly encodes the dynamic mechanism that satisfies Newton's second law.
[0033] 4.4 Stiffness estimate obtained from step 4.2 As input, calculate the stiffness monotonic loss. :
[0034]
[0035] in, and These are the predicted stiffness values for adjacent time steps.
[0036] 4.5 Calculation of theoretical damage :
[0037]
[0038] in, For bellows in The cumulative number of fatigue cycles that have been experienced over time. This refers to the total fatigue life (or the number of limit cycles) of the specimen under specific experimental conditions. and The results were obtained from a bellows fatigue testing machine within a metal bellows degradation test system.
[0039] 4.6 Obtained from step 2.2 As input, calculate fatigue constraint loss :
[0040]
[0041] in, It is the high-dimensional feature vector output by the feature extractor. To reduce scalar damage The projection function mapped to the feature space.
[0042] 4.7 Calculate the total physical constraint loss based on the results obtained from steps 4.3, 4.4, and 4.6. :
[0043]
[0044] in, The weights are the hyperparameters for the loss. At different stages of training or for data with different noise levels, the model's dependence on specific physical laws can be dynamically changed by adjusting the weights.
[0045] 5. Calculate the double ellipsoidal regression loss (Reference Figure 3 )
[0046] 5.1 High-dimensional latent feature vector obtained from step 2.2 As input, calculate the generalized Mahalanobis distance. :
[0047]
[0048] in, Denotes the center of the ellipsoidal space, a positive definite matrix. The metric matrix represents the shape of an ellipsoid in high-dimensional space. The inverse matrix corresponds to the covariance matrix of the characteristic distribution.
[0049] 5.2 To further advance the DeepESVDD algorithm from anomaly detection to remaining lifetime prediction, a double ellipsoidal boundary mechanism is proposed, such as... Figure 3 As shown. Unlike traditional SVDD which only focuses on a single anomaly decision boundary, this mechanism constructs two key topological boundaries in the feature space: the inner ellipsoidal boundary. and the boundary of the outer ellipsoid Their corresponding radii are respectively and .
[0050] Inner ellipsoid boundary From radius Define, satisfy the set This boundary is determined by health sample data from the early stages of bellows service, i.e., data with zero fatigue loading cycles, representing the steady-state operating space of the system.
[0051] outer ellipsoid boundary ( ) by radius Define, satisfy the set This boundary is fitted from critical failure samples, i.e., data with an upper limit to the number of fatigue loading cycles, and represents the functional damage boundary of the bellows.
[0052] 5.3 Based on the results obtained in steps 5.1 and 5.2 , , Calculate health indicators :
[0053]
[0054] in, Let be a linear saturation function, defined as follows:
[0055]
[0056] Linear saturation function The introduction of defines the physical mechanism boundary of the algorithm, when hour, This indicates that the bellows is in brand new, healthy condition. hour, This indicates that the bellows has reached the end of its lifespan. At that time, HI decreased monotonically with the increase of fatigue loading cycles.
[0057] 5.4 Based on the results obtained in steps 5.1 and 5.2 , , Calculate the geometric boundary penalty term :
[0058]
[0059] Geometric boundary penalty term Make healthy samples Use matrices as much as possible The transformation falls into the inner ellipsoid Inside, and the failed sample Close to the outer ellipsoid Boundaries, realizing the geometric shape matrix of the feature space. Metric learning.
[0060] 5.5 Based on the source domain dataset from step 3.2 Remaining life label in The health indicators obtained in steps 5.3 and 5.4 Calculate the geometric boundary penalty term Calculate the regression loss of the double ellipsoid :
[0061]
[0062] The first term is the prediction error term, which is used to minimize the predicted lifetime calculated based on the generalized Mahalanobis distance. Compared to actual lifespan The error between them. Second item. This is a geometric boundary penalty term used to accelerate convergence and maintain the stability of the geometric structure in high-dimensional space.
[0063] 6. Calculate the final total loss of the optimization objective based on the results obtained from steps 3.2, 4.7, and 5.5. :
[0064]
[0065] in, To combat losses The weight, For physical mechanism loss The weight. It is a weighted unification of the aforementioned physical, geometric, and adversarial constraints, encompassing regression accuracy, domain adaptability, and physical consistency.
[0066] 7. Reverse update the PCADA-DED network parameters to... Minimize as the objective, with a fixed discriminator parameter The gradient descent method is used to synchronously update the feature extractor. Physical regression branch and geometric parameters shape .
[0067] 8. Repeat steps 2 to 7 of the K-round loop, continuously updating the PCADA-DED network parameters until... It tends to stabilize, that is, the computation converges. The optimal solution is reached. The final optimized network is retained. parameter and geometric parameters .
[0068] 9. Lightweight deployment of models (see...) Figure 1 )
[0069] This invention proposes a training-inference decoupling algorithm deployment strategy. During the model training phase, due to the domain discriminator... Feature alignment has been completed, and the physical mechanism is as follows: Gradient backpropagation is internalized in the feature extractor In the weight distribution, prune these two computational branches, retaining only the feature extractor. Finally, the pruned model, along with the dual ellipsoidal support vector calculation module DE-SVDD, is deployed on a high-performance edge processor that also provides storage functionality.
[0070] 10. Real-time lifetime prediction calculation (see...) Figure 4 )
[0071] Vibration data of the metal bellows in the pipeline under unknown new working conditions is collected online and sent to the edge computing processor deployed in step 9 for calculation, and finally the remaining lifespan y of the bellows at the current time t is obtained.
[0072] The present invention also provides a system for implementing the above method, the system comprising: at least one sensor for data acquisition, a data acquisition unit (DAQ), and an edge processor configured to perform both storage functions and to execute algorithms stored in memory, to complete all the steps of the above method.
[0073] The beneficial effects of this invention are as follows:
[0074] 1. This invention effectively solves the distribution shift problem under varying operating conditions through adversarial transfer learning. Experiments show that in cross-velocity prediction tasks, the root mean square error (RMSE) is significantly reduced, successfully eliminating the data distribution differences caused by changes in operating conditions. This allows the model to maintain extremely high RUL prediction accuracy and robustness when facing unknown and changing target domain operating conditions.
[0075] 2. By incorporating prior physical laws such as dynamics and stiffness monotonicity as strong constraints into the deep learning model, the degradation trajectory of the life prediction is ensured to be smooth and monotonic, fully conforming to physical reality. This fundamentally solves the problem of disordered fluctuations and violation of physical intuition in the prediction results of pure data-driven models, greatly enhancing the credibility of the prediction results and enabling them to be used as a reliable basis for maintenance decisions.
[0076] 3. Through an innovative training-inference separation deployment strategy, the complex physical adversarial model in the training phase was successfully optimized into a lightweight edge model in the inference phase, achieving millisecond-level inference latency on embedded edge devices, thus meeting the needs of industrial real-time monitoring. Attached Figure Description
[0077] Figure 1 This is a diagram illustrating the deployment framework of the PCADA-DED method and system of the present invention.
[0078] Figure 2 This is a flowchart illustrating the Physical Information Feature Learning (PIFL) module in this invention. Figure 3 This is a schematic diagram of the calculation process for the dual ellipsoidal support vector data description (DE-SVDD) in this invention; Figure 4 This is a flowchart of an embodiment of the present invention; Figure 5 This is a schematic diagram of the bellows degradation test system according to an embodiment of the present invention;
[0079] Figure 6 The training loss function curve for the C4 case is shown.
[0080] Figure 7 Error distribution diagram for case C4;
[0081] Figure 8 Box plot of the C4 case distribution;
[0082] Figure 9 The degradation trajectory plots on C4 are shown for different comparison methods in the C4 case. Detailed Implementation
[0083] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.
[0084] Example: Method and System for Predicting Remaining Life of Bellows under Variable Flow Conditions
[0085] To fully verify the effectiveness of the PCADA-DED framework proposed in this invention in addressing the challenge of predicting the remaining service life (RUL) of metal bellows across operating conditions and its feasibility for deployment at the industrial edge, this embodiment constructs a bellows fatigue life degradation simulation test bench and conducts discrete degradation experiments throughout the entire life cycle.
[0086] The method flow of this invention embodiment is as follows (see Figure 4 ):
[0087] Step 1: Set up the experimental system (participate) Figure 5 )
[0088] The example selected a certain type of metal bellows with a designed fatigue life of approximately 600 cycles as the research object. To realistically reproduce the physical field environment of mechanical fatigue damage accumulation and fluid-structure interaction vibration faced by the bellows during service, a combined test platform including an electro-hydraulic servo fatigue testing machine and a fluid circulation vibration test bench was built.
[0089] See test system Figure 5 The equipment shown includes at least the following: test piping loop, DN50 metal corrugated pipe test specimen, water pump, vibration sensor, data acquisition unit, frequency converter, flow meter, water storage tank, and corrugated pipe fatigue testing machine.
[0090] The assembly and operation of the test system are not described in detail, but it includes at least the following characteristics:
[0091] 1. The system should be able to provide real-time triaxial vibration signals of the bellows under varying flow parameters, requiring high-frequency data sampling. In this embodiment, the adjustable flow rates are 20, 30, 40, and 50 L / min, with a data acquisition frequency of 10 kHz.
[0092] 2. To verify the robustness of the method of the present invention to different fluid conditions and individual differences, two independent specimens from different production batches were selected for the experiment (labeled as specimen A and specimen B, respectively).
[0093] 3. It can induce displacement fatigue damage in bellows, and the magnitude, speed, and number of fatigue cycles are adjustable and recordable. In this embodiment, test specimens A and B exhibit a fatigue life of approximately 600 cycles under a displacement of ±18mm.
[0094] 4. The test bellows can be easily installed and removed from the test piping loop and the bellows fatigue testing machine. This embodiment uses a flange connection.
[0095] 5. The operating medium is a fluid, and the flow of the medium causes the metal bellows to generate vibration signals. In this embodiment, the test medium is water.
[0096] Step 2: Experimentation and Data Acquisition
[0097] The experiment employed an intermittent testing strategy combining offline fatigue loading and online vibration monitoring. First, a brand-new bellows was installed on a fluid test bench, and its original vibration signals were collected as a baseline for its health condition.
[0098] Subsequently, the specimen was moved to a fatigue testing machine and subjected to 50 axial compression cycles to introduce early damage, before being returned to the fluid testing bench for condition monitoring. During the monitoring phase, a high-sensitivity triaxial piezoelectric accelerometer was used to acquire the vibration response signal of the bellows, with a sampling frequency set to 10 kHz, and data was continuously acquired for at least 30 seconds each time. A Keysight high-performance data acquisition instrument and computer terminal were preferred for real-time acquisition of the vibration signals.
[0099] Repeat the above "load-monitor" process until the specimen experiences fatigue fracture or leakage, thus forming a complete life cycle dataset.
[0100] To verify the robustness of the method of this invention to different fluid conditions and individual differences, two independent specimens from different production batches (labeled as specimen A and specimen B, respectively) were selected for the experiment, and four different flow rate conditions (20, 30, 40, and 50 L / min) were set. The acquired raw long-sequence signals were preprocessed by slicing using a non-overlapping sliding window strategy with a window size of 2048 and a step size of 2048, reconstructing the continuous signals into a standard 3×2048 input matrix.
[0101] To comprehensively evaluate the generalization robustness of the PCADA-DED framework, a bidirectional multi-condition cross-validation scheme was designed. Among the four flow rate conditions, one was selected sequentially as the unknown target domain, while the remaining three were mixed as labeled source domains. Simultaneously, two specimens were alternately selected as the source and target domains to verify the model's transferability across manufacturing individual differences. Thus, eight independent cross-domain transfer cases (C1 to C8) were constructed, as shown in Table 1 below. The final performance evaluation result is the average of these eight cases to ensure the objectivity and reliability of the conclusions.
[0102] Table 1 Cross-Domain Migration Case Configuration Table
[0103]
[0104] Step 3: PCADA-DED Model Training
[0105] The test conditions in this embodiment are as follows: Test condition A (flow rate {20, 30, 40} L / min) is the source domain data. (Number of fatigue events tagged) The test specimen under condition B (flow rate 50 L / min, fatigue cycles 0, i.e., vibration data under undamaged bellows conditions) is the target domain data. The model was trained using data from test specimen A under operating conditions and a small amount of data from test specimen B under operating conditions, and the full life cycle fatigue life of test specimen B under a flow rate of 50 L / min was predicted across domains.
[0106] This embodiment preferably uses a feature extractor. It is composed of a concatenated convolutional neural network and a long short-term memory neural network (CNN-LSTM), and the specific training process is shown in Table 2 below:
[0107] Table 2 PCADA-DED Training Process Table
[0108]
[0109] Step 4: Algorithm Deployment of the Model
[0110] 1. The training of the PCADA-DED model algorithm in this embodiment is performed on a high-performance computing platform equipped with an Intel Core i7-12650H processor and an NVIDIA GeForce RTX4060 graphics card, running on a Linux operating system environment, and the model architecture is built based on the PyTorch deep learning framework.
[0111] 2. Prune the trained PCADA-DED model, retaining only the feature extractor. The DE-SVDD part of the dual ellipsoidal support vector computation module is deployed with half-precision quantization at the NVIDIA Jetson AGX Orin edge based on the TensorRT engine.
[0112] Step 5: Comparative Analysis and Evaluation Indicators
[0113] To analyze the performance advantages of the PCADA-DED framework of this invention from multiple dimensions, and to verify the unique contributions of physical mechanisms and adversarial adaptive transfer learning in cross-domain prediction, six benchmark methods were constructed for comparison, including:
[0114] CNN-LSTM: As a performance reference for non-transfer deep learning, this model is trained under supervision only on the source domain and applied directly to the target domain.
[0115] TCA: A classic shallow transfer learning method that narrows the marginal distribution distance by minimizing the maximum mean difference (MMD).
[0116] DANN: A standard method for deep adversarial transfer learning, which achieves global distribution alignment through a mini-maximum game between the domain discriminator and the feature extractor.
[0117] CDAN: One of the current state-of-the-art (SOTA) methods for unsupervised domain adaptation, employing a conditional discriminator to capture more fine-grained multimodal structures.
[0118] P-DED: An ablation variant of the present invention that retains only the Physical Constraints (PIFL) and the dual ellipsoidal regression module, while removing the adversarial domain adaptive branch, in order to verify the effectiveness of the pure physical constraints.
[0119] ADA-DED: Another ablation variant of the present invention removes the physical constraint module to verify the effectiveness of simply performing statistical alignment without physical prior guidance.
[0120] To quantitatively evaluate the accuracy, goodness of fit, and physical consistency of the prediction results, three core evaluation metrics are used:
[0121] Root mean square error (RMSE): Measures the average deviation between predicted lifetime and actual lifetime.
[0122]
[0123] in For the number of test samples, For true RUL, To predict RUL.
[0124] Coefficient of determination (R²): Evaluates the model's ability to explain the degradation trend; the closer to 1, the better the fit.
[0125]
[0126] Monotonicity: measures the degree of conformity between the predicted trajectory and physical reality. The value range is [0,1]. The closer it is to 1, the smoother the trajectory is and the monotonically decreasing, which conforms to the fatigue accumulation law.
[0127]
[0128] in, For the number of test samples, For the first The time step of the trajectory. For standard symbolic functions, the definition is:
[0129]
[0130] Step 6: Analysis of Calculation Results
[0131] 1. Overall performance and multi-dimensional indicator analysis
[0132] The average values of RMSE, R², and monotonicity indices for each comparison method in eight cross-domain migration cases show that the PCADA-DED proposed in this invention significantly outperforms all other comparison methods in all metrics.
[0133] RMSE: The average RMSE of the CNN-LSTM model is as high as 89.4, indicating that unprocessed domain offset leads to a severe performance degradation. The average RMSE of the P-DED model, which only includes physical constraints, is 78.7, proving that physical constraints alone are insufficient to correct feature distribution misalignment caused by changes in working conditions. The ADA-DED model, which only includes adversarial learning, reduces the average RMSE to 39.4, outperforming the mainstream transfer learning method CDAN (42.1), proving that adversarial adaptation under dual ellipsoidal metrics has excellent alignment capabilities. The present invention, PCADA-DED, combines the advantages of both, further reducing the average RMSE to 28.1, proving that physical constraints, by limiting the feature search space, assist the adversarial network in finding a more fundamental and robust degenerate manifold. The RMSE metrics of each comparative method under different cases are shown in Table 3.
[0134] Table 3. RMSE indices for each comparison method under different operating conditions.
[0135]
[0136] R 2 The PCADA-DED method achieves an average R² of 0.97, and even in the most challenging high-velocity extrapolation condition (C4), it maintains an R² of 0.95. This is primarily attributed to the anisotropic metric space constructed by DE-SVDD, which effectively filters out noise components unrelated to the degradation direction. The comparison methods under different conditions... The indicators are shown in Table 4.
[0137] Table 4 Comparison methods under different working conditions
[0138]
[0139] Monotonicity: While the RMSE performance of purely data-driven adversarial methods (DANN, CDAN, ADA-DED) is acceptable, their monotonicity indices hover only between 0.74 and 0.80, indicating that their predicted trajectories contain numerous non-monotonic oscillations that violate physical principles. In stark contrast, the P-DED and PCADA-DED models, which incorporate physical constraints, achieve average monotonicities of 0.96 and 0.98, respectively. This confirms that the stiffness monotonicity constraint in the PIFL module has been successfully internalized as a strong inductive bias in the model, forcing the model output to conform to a degenerate trend consistent with physical logic. The monotonicity indices of each comparative method under different operating conditions are shown in Table 5.
[0140] Table 5 Monotonicity indices of each comparison method under different operating conditions
[0141]
[0142] 2. Analysis of Degradation Mechanism and Physical Consistency in Typical Cases
[0143] To more intuitively reveal the model's predictive behavior and physical robustness under extremely complex operating conditions, and to visualize and analyze the results, a highly challenging case, C4, was selected as a typical research object. This case not only involves the transfer of manufacturing differences across individuals, but also covers extrapolating predictions to unknown high-flow-rate conditions of 50 L / min. The strong fluid-structure interaction effect makes it a typical example for testing the generalization boundary of the algorithm.
[0144] Training process: Figure 6 The dynamic evolution trajectory of the total loss function and the RMSE of the target domain test set during training is shown. The training loss curve of the model exhibits a stable convergence trend, without gradient explosion or non-convergence, proving that the optimization strategy proposed in this invention can effectively reconcile the competition between physical constraints and adversarial transfer learning.
[0145] Prediction accuracy:
[0146] Figure 7 The probability density distribution of the prediction error in case C4 was statistically analyzed. The histogram shows a sharp Gaussian distribution centered at zero. No significant long-tail effect or skewness was observed. On the target domain test set of case C4, the scatter plots of predicted and true values clustered closely around the ideal regression line, with an R² as high as 0.954. The probability density of the prediction error exhibited a sharp Gaussian distribution centered at zero, demonstrating that the model successfully overcame the systematic bias caused by domain shift.
[0147] Predicted stability:
[0148] Figure 8Box plots of prediction errors were generated every 50 cycles. In the early stages of service (0-200 cycles), due to the weak damage characteristics, traditional models are highly susceptible to significant fluctuations caused by fluid noise. However, thanks to the inner ellipsoidal boundary in the PIFL module… Under the constraints of the outer ellipsoid boundary, the predicted distribution of PCADA-DED remained flat and compact, with no false alarms. Even at the end of the lifetime (500-600 cycles), the stage of most rapid crack propagation and strongest nonlinear characteristics, the interquartile range (IQR) of the predicted distribution remained convergent. This confirms the outer ellipsoid boundary... The PCADA-DED model effectively regulates the characteristic divergence of the failure critical point, ensuring consistent confidence levels in the prediction results throughout the entire lifecycle. This demonstrates that PCADA-DED not only provides accurate predictions overall but also exhibits extremely high robustness at all stages of the lifecycle, overcoming the shortcomings of traditional models that are prone to severe fluctuations at the end of degradation.
[0149] Predicted trajectory:
[0150] Figure 9 By comparing the full-lifecycle degradation trajectories generated by different algorithms, the core value of physical constraints is intuitively demonstrated. Comparing the full-lifecycle degradation trajectories generated by different algorithms, the curves of purely data-driven methods such as CNN-LSTM, TCA, and DANN exhibit severe sawtooth fluctuations, and even show the anti-physical phenomenon of RUL increasing over time. In contrast, the trajectory generated by PCADA-DED in this invention exhibits an extremely smooth and strictly monotonically decreasing trend. Especially in the rapid degradation stage from 300 to 600 cycles, the model not only accurately tracks the trend of accelerated failure but also completely eliminates non-monotonic fluctuations, perfectly matching the real physical degradation path. This proves that the model can still adhere to the physical principle of irreversible damage even in noisy environments.
[0151] 3. Performance verification of edge computing deployment
[0152] To verify the algorithm's ability to perform real-time monitoring in industrial settings, the trained model was deployed on an NVIDIA Jetson AGX Orin 64GB edge computing platform using the NVIDIA TensorRT inference engine. Specifically, post-training quantization (PTQ) was employed, converting the model weights from FP32 to FP16. The experimental results are shown in Table 6 below.
[0153] Table 6: Comparison of inference performance across different hardware platforms
[0154]
[0155] The results show that the TensorRT-optimized model has a single inference latency of only 2.8 milliseconds and a throughput of 357 FPS on Jetson AGX Orin, fully meeting the needs of real-time monitoring in industrial settings. More importantly, its energy efficiency ratio (13.7 FPS / W) is improved by approximately 42% compared to high-performance workstations, and FP16 quantization reduces model memory usage by approximately 50% with almost no loss of accuracy.
[0156] In summary, the PCADA-DED method proposed in this invention outperforms all comparable methods in both theoretical and practical bellows RUL prediction performance. It not only achieves high-precision, highly physically consistent predictions in cross-condition migration tasks, but also demonstrates low-latency, high-energy-efficiency engineering practical value on resource-constrained edge devices, providing a feasible solution for the intelligent operation and maintenance of complex electromechanical equipment that balances high accuracy and computational efficiency.
[0157] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for predicting the remaining life of a metal bellows, characterized in that, Includes the following steps: S1. Obtain the vibration acceleration signal of the metal bellows and construct a source domain dataset containing labeled known working condition data. and the target domain dataset containing unlabeled work condition data to be predicted ; S2. Based on the source domain dataset and the target domain dataset, train a PCADA-DED prediction model; the model includes a feature extractor. Domain discriminator Physical regression branch And the dual ellipsoidal support vector data description DE-SVDD module; the physical regression branch For use according to the feature extractor The output is used to calculate the stiffness estimate; Training is achieved by minimizing the total loss function. conduct, ;in For double ellipsoidal regression loss, To counteract domain adaptation loss, The total physical constraint loss; the feature extractor The parameter update is simultaneously affected by , and Gradient supervision; S3. After the model training converges, remove the domain discriminator. and the physical regression branch The feature extractor is retained. Together with the DE-SVDD module, they form a lightweight deployment model and are deployed on edge computing devices; S4. The vibration acceleration signal collected in real time is processed using the deployment model to output the remaining life prediction value.
2. The method according to claim 1, characterized in that, In step S2, the adversarial domain adaptation loss The calculation method is as follows: ; During model training, by maximizing Update the domain discriminator The parameters, and by minimizing Update the feature extractor The parameters.
3. The method according to claim 1, characterized in that, In step S2, the total physical constraint loss The calculation method is as follows: ;in, The loss is based on the residuals of the dynamic equation. To constrain stiffness estimation Loss that decreases monotonically over time. The loss is the correlation between constraint characteristics and theoretical damage; the stiffness estimate From the physical regression branch Based on the feature extractor output The calculation is performed, and the Softplus activation function ensures that the value is always positive. The weight hyperparameters for the loss.
4. The method according to claim 1, characterized in that, In step S2, the DE-SVDD module is based on the generalized Mahalanobis distance. Building health indicators The generalized Mahalanobis distance The calculation method is as follows: ; Where M is a positive definite metric matrix; the health indicators ; in, It is a linear saturation function, defined as follows: when the input value is ≤0, the output is 0; when the input value is ≥1, the output is 1; when the input value is between (0,1), the output is the original value. , These are the inner ellipsoid boundary radius and the outer ellipsoid boundary radius, respectively.
5. The method according to claim 4, characterized in that, In step S2, the double ellipsoidal regression loss The calculation method is as follows: ; in, The geometric boundary penalty term is calculated as follows: ; Normal and Failure represent the set of healthy samples and the set of critically failed samples in the source domain, respectively.
6. The method according to claim 4 or 5, characterized in that, During model training in step S2, the radius of the inner ellipsoid boundary... and the radius of the outer ellipsoid boundary Based on the generalized Mahalanobis distance between healthy samples and critical failure samples in the source domain data The statistical quantiles are dynamically updated.
7. The method according to claim 1, characterized in that, Step S1 is followed by step S1a: numerically integrating the vibration acceleration signal to obtain a system state vector containing acceleration, velocity, and displacement, which is used for the total physical constraint loss. Calculation of dynamic loss in the middle.
8. The method according to claim 1, characterized in that, In step S3, the lightweight deployment further includes a quantization step of converting the weight parameters of the deployment model from FP32 precision to FP16 precision.
9. A system for predicting the remaining life of a metal bellows, used to implement the method according to any one of claims 1 to 8, characterized in that, include: The data acquisition module includes a vibration acceleration sensor for acquiring vibration signals; A data processing module is used to execute the training and prediction steps of the method. An edge computing platform is used to host and run the data processing module and the deployment model.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 8.