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Fusing Physics-based and Deep Learning Models for Prognostics
Manuel Arias Chao, Chetan Kulkarni, Kai Goebel, Olga Fink
TL;DR
Physics-based prognostics can be incomplete, while data-driven models are constrained by limited dataset representativeness. The paper fuses calibrated physics-based health information with sensor readings as deep-learning inputs, and reports a 127% average extension in prediction horizon with less training data.
Problem
Physics-based models may be incomplete for complex systems, while data-driven prognostics require representative training datasets that are difficult to obtain.
Method
The framework calibrates a physics-based performance model to infer health-related parameters and combines them with sensor readings as inputs to a deep neural network.
Results
127% average prediction-horizon extension was achieved compared with pure data-driven methods on nine turbofan engines under real flight conditions.
Takeaways & Limitations
The hybrid framework produced accurate and robust failure-time predictions, required less training data, and remained robust to limited training-dataset representativeness.
Takeaways & Limitations
Transferability to other problems remains a future research direction, especially when only limited physics-based information is available.
Abstract
from arXiv · showhide
Physics-based and data-driven models for remaining useful lifetime (RUL) prediction typically suffer from two major challenges that limit their applicability to complex real-world domains: (1) incompleteness of physics-based models and (2) limited representativeness of the training dataset for data-driven models. Combining the advantages of these two directions while overcoming some of their limitations, we propose a novel hybrid framework for fusing the information from physics-based performance models with deep learning algorithms for prognostics of complex safety-critical systems under real-world scenarios. In the proposed framework, we use physics-based performance models to infer unobservable model parameters related to a system's components health solving a calibration problem. These parameters are subsequently combined with sensor readings and used as input to a deep neural network to generate a data-driven prognostics model with physics-augmented features. The performance of the hybrid framework is evaluated on an extensive case study comprising run-to-failure degradation trajectories from a fleet of nine turbofan engines under real flight conditions. The experimental results show that the hybrid framework outperforms purely data-driven approaches by extending the prediction horizon by nearly 127\%. Furthermore, it requires less training data and is less sensitive to the limited representativeness of the dataset compared to purely data-driven approaches.
1 Introduction
Physics-based prognostics are limited by incomplete understanding of complex degradation, while data-driven methods depend on representative failure datasets that are difficult to collect. The paper proposes combining calibrated physics-based health features with sensor data in a deep learning prognostics framework and evaluates it on nine turbofan engines.
- Motivation: Physics-based models have limited practical applicability because degradation processes are well understood mainly for critical or relatively simple components.
- Motivation: Representative training datasets are difficult to collect because failures are rare and operating environments and mission profiles create diverse degradation trajectories.
- Motivation: Hybrid modeling combines physics-based interpretability and data-generation capabilities with deep learning’s ability to discover complex patterns from data.
- Proposed framework: The proposed framework infers health-related model parameters and virtual sensors from calibrated thermodynamic performance models, then adds them to condition-monitoring sensor inputs.
- Evaluation: The framework is evaluated using run-to-failure trajectories from nine turbofan engines under real flight conditions, including limited representation of test degradation conditions in training data.
- Results: The hybrid framework requires less training than purely data-driven algorithms.
2 Background
The background formulates prognostics around calibrating physics-based performance models from condition-monitoring observations and learning reliable RUL mappings. The dataset combines operating conditions, multivariate sensor time series, labels, and reference system-model responses for a fleet of units.
- Physics-based models: Thermodynamic performance models represent physical system behavior and can predict measured process variables and unmeasured system and subsystem performance.
- Calibration: Calibration is an inverse problem that infers model parameters so the physics-based model response follows observed system data.
- Calibration: Because full posterior calibration is computationally expensive, the approach commonly uses point estimates such as maximum a posteriori estimation.
- Problem formulation: The available dataset contains operating conditions, multivariate condition-monitoring sensor readings, and RUL labels from N units with potentially different signal lengths.
- Problem formulation: Each unit is modeled as undergoing normal linear degradation before an abnormal condition leads to failure at its end-of-life time.
- Problem formulation: The prognostics task is to learn a predictive model that provides reliable RUL estimates for a test dataset of M units.
3 Proposed Framework: Deep Learning-Based Prognostics with Physics-Inferred Inputs
The proposed framework calibrates a physics-based performance model to infer health-related features, then combines them with operating conditions and sensor information for deep-learning prognostics. It is designed to improve interpretability, data efficiency, and robustness when training data are sparse or incomplete.
- The framework combines a calibrated physics-based performance model with deep learning to obtain hybrid prognostics models.
- Calibration estimates unobservable model parameters that encode subcomponent deterioration and provides high-confidence estimates of unobserved process variables.The calibrated model is F(w, ˆθ), where ˆθ denotes inferred parameters and ˆxv denotes virtual sensors.
- The hybrid method enhances raw condition-monitoring data with health-related features before learning a mapping from the enhanced input to RUL.The standard data-driven mapping uses [w, xs], whereas the hybrid representation adds [ˆxs, ˆxv, ˆθ].
- The prognostics network receives operating conditions, estimated monitoring signals, virtual sensors, and unobservable model parameters as inputs.Figure 2 depicts a CNN prognostics model and UKF-based calibration using a discrete-time counterpart of the physics-based model.
- 3.1 Calibration of the System Performance Model: UKF calibration uses a state-space formulation in which health parameters are modeled as a random walk and measurements depend on current states and inputs.
- 3.1 Calibration of the System Performance Model: A deep-neural-network simulator approximates the discrete-time dynamic transition used to speed UKF learning, while a separate deep network learns the prognostics mapping.
4 Case Study
The case study evaluates the hybrid prognostics framework on nine turbofan engines with varied degradation and flight conditions. It combines condition-monitoring data with physics-model outputs and assesses deep learning models using standardized preprocessing and RUL metrics.
- 4.1 A Small Fleet of Turbofan Engines: The dataset contains nine turbofan engines with unknown, different initial health conditions and run-to-failure degradation trajectories.It was generated with the C-MAPSS dynamical model using recorded commercial-jet flight conditions.
- 4.1 A Small Fleet of Turbofan Engines: Test units 14 and 15 have shorter, lower-altitude flight distributions than the training units, creating limited representation of their operating conditions.The fleet includes six training units and three test units.
- 4.1 A Small Fleet of Turbofan Engines: The fleet includes two failure modes: isolated HPT-efficiency degradation and combined LPT-efficiency, LPT-flow, and HPT-efficiency degradation.Units 2, 5, and 10 exhibit the first mode, while units 16, 18, 20, 11, 14, and 15 exhibit the more complex mode.
- 4.1 A Small Fleet of Turbofan Engines: The dataset is sampled at 0.1 Hz, with 0.53M samples for model development and 0.12M samples for testing.Test unit 14 has the lowest flight time but the largest number of flight cycles.
- 4.2 Pre-processing: The hybrid model uses 50 inputs, adding model predictions, calibration parameters, and virtual sensors to the 20 inputs used by data-driven models.Inputs are normalized to [−1, 1], and CNN inputs use sliding windows of size N_tw = 50 with stride 1.
- 4.3 Deep Learning Prognostics Model: The study compares FNN and CNN prognostics models and evaluates them with RMSE and NASA’s scoring function.The comparison targets the hybrid framework against purely data-driven approaches.
5 Experimental Results
The hybrid approach consistently outperformed purely data-driven baselines across RUL estimation, prediction horizon, dataset-size, feature-ablation, and calibration-quality analyses. Physics-derived features improved performance, with calibration parameters providing the most informative additions, while calibration uncertainty was also examined.
- 5.1 RUL Estimation: 16%–47% lower RMSE and 21%–68% lower s-score were achieved by the hybrid approach, depending on the neural-network model.The larger s-score reduction indicates more effective handling of RUL over-estimation; the hybrid CNN was the best-performing model.
- 5.1 RUL Estimation: 127% average prediction-horizon improvement was obtained while maintaining similar prediction accuracy across the test fleet.The horizon measures the interval from the time errors remain within 5 cycles until end of life.
- 5.2.1 Ablation Study I: Impact of Dataset Size: 38% better RMSE was observed for CNN than FNN within the purely data-driven comparison, while the hybrid approach outperformed the baseline with either architecture.The dataset-size analysis emphasized the difficulty of learning representative degradation features from limited condition-monitoring data.
- 5.2.2 Ablation Study III: Impact of Physics-Derived Information: Adding physics-derived features always improved prediction performance, but optimal performance required including calibration factors θ.The ablation used perfect calibration to isolate the contribution of de-noised sensors, virtual sensors, and calibration factors.
- 5.2.2 Ablation Study III: Impact of Physics-Derived Information: Calibration parameters θ were the most informative input features for RUL prediction, followed by features representing operating conditions.Figure 7 ranks the top nine inputs using normalized mutual information with the RUL target.
- 5.2.3 Impact of Calibration Quality: The calibration-quality study evaluated noisy and biased estimates of θ to assess their impact on hybrid prognostics performance.Noise levels of SNRdb = 20 and SNRdb = 15, plus shifts α = −0.5 and α = 0.5, were considered.
6 Conclusions
The paper concludes that fusing calibrated physics-model information with sensor readings in a deep neural network yields accurate and robust RUL prognostics. On nine turbofan engines under real flight conditions, the framework extended prediction horizons by 127% on average and required less training data, while transferability remains a future research direction.
- 6 Conclusions: The framework infers health-related physics-model parameters through calibration and combines them with sensor readings as deep-network inputs.This creates a hybrid prognostics model for complex-system RUL prediction.
- 6 Conclusions: 127% longer prediction horizons were achieved on average than with pure sensor-data-driven methods on nine turbofan engines under real flight conditions.The evaluation used synthetic run-to-failure trajectories generated with the C-MAPSS dynamical model.
- 6 Conclusions: Less training data was required than for purely data-driven algorithms.
- 6 Conclusions: Performance remained robust to calibration uncertainty and to testing units with operating conditions dissimilar from those represented in training.
- 6 Conclusions: Transferability to other problems remains a future direction requiring complete physics-based models and sensor readings informative about system state.The paper also identifies methods for settings with only limited physics-based information as a future direction.