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Hybrid deep fault detection and isolation: Combining deep neural networks and system performance models

Manuel Arias Chao, Chetan Kulkarni, Kai Goebel, Olga Fink

arXiv:1908.01529v2eess.SYcs.SY

TL;DR

Fault diagnostics is difficult when only healthy data are available, fault types are unknown, and changing conditions mask fault signatures. The paper combines calibrated physics-based performance models with deep-learning diagnostics, using inferred variables and parameters to enrich the input representation. On C-MAPSS flight-condition data, the hybrid approach outperforms pure data-driven methods for detection and isolation, particularly under high operating variability.

  • Problem

    Fault detection and isolation must operate with only healthy data, unknown fault classes, changing operating conditions, and correlated signals that can mask fault sources.

    Source: §1 · p. 2

  • Method

    The framework calibrates a physics-based performance model and feeds inferred measured variables, virtual sensors, and model parameters into a deep-learning diagnostics model.

    Source: §3.1 · p. 5

  • Results

    The hybrid framework outperforms pure data-driven deep-learning methods for fault detection and isolation, particularly under high variability of operating conditions.

    Source: §1 · p. 3, §7 · p. 19

  • Takeaways & Limitations

    The calibrated hybrid representation reduces smearing and enables precise isolation of the affected signal in the evaluated setting.

    Source: §1 · p. 3, §8 · p. 19

    Fault isolation depends on calibrated models representing the fault modes accurately; unrepresented faults may reduce isolation capability.

    Source: §8 · p. 20

Abstract

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With the increased availability of condition monitoring data and the increased complexity of explicit system physics-based models, the application of data-driven approaches for fault detection and isolation has recently grown. While detection accuracy of such approaches is generally good, their performance on fault isolation often suffers from the fact that fault conditions affect a large portion of the measured signals thereby masking the fault source. To overcome this limitation and enable a more accurate fault detection, we propose a hybrid approach combining physical performance models with deep learning algorithms. Unobserved process variables are inferred with a physics-based performance model to enhance the input space of a data-driven diagnostics model. To validate the effectiveness of the proposed method, we generate a condition monitoring dataset of an advanced gas turbine during flight conditions under healthy and four faulty operative conditions based on the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dynamical model. We evaluate the performance of the proposed method in combination with two different deep learning algorithms: feed forward neural networks and Variational Autoencoders, both of which demonstrate a significant improvement when applied within the hybrid fault detection and diagnostics framework. The proposed method is able to outperform pure data-driven solutions, particularly for systems with a high variability of operating conditions. It provides superior results both for fault detection as well as for fault isolation. For fault isolation, it overcomes the smearing effect that is observed in pure data-driven approaches and enables a precise isolation of the affected signal. We also demonstrate that deep learning algorithms provide a better performance on fault detection compared to the traditional machine learning algorithms.

1 Introduction

The paper addresses fault detection and isolation when only healthy data are available and operating conditions vary, making fault signatures difficult to learn from correlated measurements. It proposes enriching deep-learning diagnostics with physics-based model information and evaluates the approach on simulated turbofan conditions.

1 Introduction

  • Limited labeled fault data make representative fault-pattern learning difficult, especially in safety-critical systems where faults are rare.Prior work often formulates diagnostics as classification and addresses imbalanced faulty classes.Source: §1 · p. 2
  • The study targets fault detection and isolation with only healthy-class information, unknown fault types, and frequently changing operating conditions.Aircraft engines under changing flight conditions exemplify this setting.Source: §1 · p. 2
  • Correlated condition-monitoring signals can smear fault effects across unaffected signals, making root-cause isolation difficult from residuals alone.Changing operating conditions can also mask fault characteristics when data from conditions are combined.Source: §1 · p. 2
  • The proposed framework combines physics-based models with deep learning for diagnostics under varying conditions, particularly when faulty samples are unavailable during development.It uses inferred unobserved process variables to enlarge the diagnostic input space and improve representation power.Source: §1 · pp. 2–3
  • The method is evaluated with feed-forward neural networks, Variational Autoencoders, and a vanilla autoencoder on C-MAPSS turbofan data covering healthy and four faulty operating conditions.The study compares hybrid models with pure deep learning, OC-SVM, and an alternative residual-based hybrid framework.Source: §1 · p. 3
  • The hybrid framework outperforms pure data-driven solutions, particularly under high operating-condition variability, improving both fault detection and isolation while reducing smearing.Deep learning algorithms also outperform traditional machine-learning algorithms on fault detection.Source: §1 · p. 3

2 Related work

Related work combines physics-based models and data-driven diagnostics through synthetic data, residuals, fusion, or physics-guided architectures. The proposed framework instead uses inferred virtual sensors and model parameters to expand the input space of a deep-learning FDI model.

2 Related work

  • Physics-based and data-driven approaches offer complementary strengths, motivating hybrid architectures that combine model interpretability and data-driven pattern discovery.Physics-based methods can be complex or incomplete, while data-driven methods depend on representative training data.Source: §2 · p. 3
  • Prior hybrid methods use synthetic healthy and faulty data with residuals, particle-filter fusion, or residual features supplied to traditional classifiers.Examples include building diagnostics, gas-turbine diagnostics, and turbofan SVM diagnostics.Source: §2 · p. 3
  • Residual-based diagnostics compute discrepancies between measurements and healthy-model responses, then process them with fault-detection and isolation logic.Deep-learning residual approaches can also include operating conditions as inputs.Source: §2 · p. 4
  • Physics-guided learning has also expanded inputs with physics-model outputs or embedded model information inside recurrent neural-network states.These approaches aim to improve approximation of system dynamics [17] [18].Source: §2 · p. 4
  • Unlike these architectures, the proposed framework uses inferred virtual sensors and unobservable model parameters to enhance a tailored deep-learning FDI algorithm.This representation is intended to provide information more directly useful for fault detection and isolation.Source: §2 · p. 4

3 Proposed Methodology

The methodology calibrates a nonlinear physics-based performance model and feeds its inferred measured variables, virtual sensors, and parameters into a deep-learning diagnostics model. Calibrated parameters support fault isolation by encoding component-level degradation information and reducing smearing.

3 Proposed Methodology

  • The performance model maps operating conditions and parameters to measured-property estimates and unmeasured virtual sensors.Its inputs are scenario descriptors w and model parameters θ; its outputs include ˆxs and xv.Source: §3.1 · p. 4
  • The hybrid approach combines condition-monitoring data with model-derived variables for subsequent deep-learning fault detection and isolation.The enhanced representation includes operating conditions, estimated measured signals, virtual sensors, and model information.Source: §3.1 · p. 5
  • Model calibration infers parameters ˆθ that reproduce observed signals, while providing calibrated virtual-sensor estimates and encoding degradation in model parameters.The deep-learning model receives w and [ˆxs, ˆxv, ˆθ].Source: §3.1 · p. 5
  • Component degradation is represented in a specific model parameter, which helps avoid the smearing characteristic of data-driven diagnostics and can expose sensor-reading errors.The calibrated representation also improves interpretability and robustness to sensor faults.Source: §3.1 · p. 5
  • The tailored deep-learning FDI algorithm reconstructs the calibrated extended representation and uses similarity scores for detection and isolation.Its input is x = [w, ˆxs, ˆxv, θ], with detection and isolation based on separate similarity logic.Source: §3.1 · p. 5

4 Methods

The paper formulates open-set fault detection and isolation with only partially known healthy data, combining calibrated system-model variables with deep learning to address changing operating conditions and fault smearing.

4.1 Problem Statement

  • The task is open-set diagnosis: only initial healthy conditions are known, while unknown fault types may be present in unlabeled data and emerge in an independent test set.The formulation includes evolving faults that may be undetected at development time and higher-intensity degradations for testing.Source: §4.1 · pp. 6–7
  • The diagnostic input combines operating conditions, measured signals, model-estimated sensor values, virtual sensors, and calibrated model parameters.The complete representation is denoted X and includes measured and inferred variables from the calibrated system model.Source: §4.1 · p. 6

4.2 System Model Calibration

  • System-model calibration infers correcting parameters from observations, using maximum a posteriori estimation or an Unscented Kalman Filter for nonlinear models.The calibration supplies model-derived information for the downstream diagnostic algorithm.Source: §4.2 · pp. 7–8
  • The proposed FDI logic replaces independent parameter thresholds with a combined deep-learning similarity analysis to reduce detection delay and expose ambiguous multivariate fault signatures.Thresholds may miss subtle degradation-rate changes or signatures distributed across several internal parameters.Source: §4.2 · p. 8
  • The calibration assumes an adequate physical model; substantial missing physics entangles degradation with model discrepancy, and jointly estimating both remains unaddressed.The paper notes that sequential estimation of correction parameters and discrepancy can produce smearing between them.Source: §4.2 · p. 8

4.3 Fault Detection

  • Fault detection is formulated as one-class learning from healthy data, using a learned mapping and similarity score whose threshold is set from validation errors.Embedding learning is used to support isolation, while direct input-to-target detection remains possible without an embedding.Source: §4.3 · p. 9

4.4 Fault isolation

  • Fault isolation compares component-wise autoencoder reconstruction errors with healthy validation errors, allowing deviations in measured and model-tuning variables to be localized.The hybrid autoencoder includes calibration factors and observed signals, so reconstruction deviations can implicate either measurements or model parameters.Source: §4.4 · pp. 9–10

5 Case Study

The case study evaluates hybrid diagnostics on simulated turbofan flight data, using common deep-learning architectures, multiple input representations, and separate detection and isolation metrics.

5.1 A Single Fault Mode in a Turbofan Engine

  • The C-MAPSS dataset contains healthy training flights and unlabeled/test flights with stepwise high-pressure-compressor efficiency degradation across flight conditions.Approximately 3200 healthy training points and 740 unlabeled/test points are available, with noisy operating conditions and four concatenated degrading flights.Source: §5.1 · p. 10

5.2 Pre-processing

  • Input dimensionality varies by strategy: CMBD uses 17 inputs, the residual-based model 31, and the proposed calibration-based hybrid model up to 45.The hybrid representation includes condition-monitoring signals, residuals, virtual sensors, and model calibration parameters.Source: §5.2 · p. 11

5.3 Network architectures

  • Partially supervised embedding-learning strategies use an encoder-decoder to reconstruct input signals, then feed the encoder’s latent representation z to a one-class network for target-label mapping.The common autoencoder architecture is [n, 20, 8, 20, n], where n is the input-space size, and the one-class network architecture is [20, 100, 1].Source: §5.3 · pp. 11–12

5.4 Training Set-up

  • Training uses common neural-network architectures and optimization settings across the deep-learning methods, with separate autoencoder and one-class training schedules.Optimization uses mini-batch SGD with Adam and Xavier initialization, while epoch and batch settings are specified consistently by model class.Source: §5.4 · pp. 13–14, Table 7 · p. 14

5.5 Evaluation Metrics

  • The evaluation separates unknown-fault detection from fault isolation, measuring health-state classification accuracy and identifying signals with reconstruction deviations above threshold.Detection uses binary health-state accuracy; isolation reports indices of components whose reconstruction discrepancy exceeds the defined criterion.Source: §5.5 · p. 14

6 Experimental Results

Across varying flight conditions, hybrid models improved fault detection and isolated HPC efficiency faults more precisely than condition-monitoring-only models. Expanded model-derived representations separated healthy and faulty conditions, while calibrated parameters reduced smearing of the fault signature.

6.1 Fault Detection

  • Nearly 100% detection accuracy was achieved by residual-based and calibration-based approaches, improving nearly 80% over the best condition-monitoring-only AE and about 4% over standard OC-SVM for calibration-based inputs.These results cover twelve models evaluated on fault detection.Source: §6.1 · p. 14, Table 8 · p. 14
  • Detection accuracy increased drastically when the AE using condition-monitoring inputs was trained on flight data restricted to altitudes above 25000 ft, supporting operating-condition variability as a major difficulty.Figure 11 reports accuracy evolution with dataset complexity for faults 1, 2, and 4; fault 3 was excluded because alt < 25000 ft.Source: §6.1 · p. 14, Figure 11 · p. 15
  • The similarity score increased with HPC fault severity, but the AE failed to discriminate healthy and faulty conditions for efficiency deterioration below 1.0%.The tested HPC efficiency faults ranged from -0.5% to -2.0%, with the decision threshold at s = 1.Source: §6.1 · p. 15, Figure 12 · p. 15
  • Detection accuracy decreased as calibration noise increased, although most models remained above pure data-driven performance across the evaluated SNR range.OC-SVM was most robust for SNRdb < 30, and the SNRdb scale is logarithmic.Source: §6.1 · pp. 15–16, Figure 13 · p. 16

6.2 Fault Isolation

  • Condition-monitoring and residual-based models smeared HPC degradation across related and unrelated variables, whereas calibrated hybrid inputs isolated the fault in variable 40, the HPC-efficiency correction parameter.The calibrated-input models achieved perfect isolation for the four HPC efficiency faults; the isolation table covers impacts from -0.5% to -2.0%.Source: §6.2 · p. 16, Table 9 · p. 17

6.3 Feature Representation

  • Hybrid latent spaces clustered faulty conditions away from healthy operation, while the purely data-driven representation showed overlapping healthy and faulty classes.The compared representations used calibrated variables, condition-monitoring signals, or residual signals; the first two latent dimensions were visualized.Source: §6.3 · pp. 17–18, Figure 15 · p. 18, Figure 16 · p. 18

7 Discussion

The experiments show that hybrid deep-learning diagnostics outperform pure data-driven methods for detection and isolation, especially under highly variable operating conditions. Model-inferred variables can support detection without accurate calibration, but precise isolation requires calibrated tuning parameters and therefore depends on calibration quality.

7 Discussion

  • Hybrid deep-learning diagnostics outperformed pure data-driven deep-learning methods in fault detection and isolation, particularly under highly variable operating conditions.The conclusion is based on experiments using the C-MAPSS dataset.Source: §7 · p. 19
  • Residual-based and calibrated-model approaches achieved similar detection performance because both latent spaces clearly separated healthy and faulty operating conditions.Good detection required the fault signature to be encoded in model-inferred variables such as ˆθ, δXs, or both.Source: §7 · p. 19
  • Accurate isolation requires model tuning parameters ˆθ, while the calibrated approach adds preprocessing and depends on how closely the calibrated model reproduces reality.If calibration is inaccurate, the ability to isolate failures clearly is expected to decrease.Source: §7 · p. 19
  • Residuals and calibrated model variables can be combined, yielding a diagnostic input that includes [w, ˆXs, ˆXv, ˆθ, δXs].This combined option requires both calibration and residual computation.Source: §7 · p. 19

8 Conclusions

The hybrid framework combines physical performance models with deep learning and outperforms purely data-driven deep learning and OC-SVM approaches for fault detection and isolation. Its advantages are strongest under highly variable operating conditions, while latent representations support informative fault detection and accurate isolation depends on model coverage of fault modes.

8 Conclusions

  • Perfect detection accuracy and precise root-cause isolation outperform purely data-driven deep learning algorithms and OC-SVM on the C-MAPSS dataset.The evaluation used simulated advanced gas-turbine flight-condition data with healthy and four faulty operative conditions.Source: §8 · p. 19
  • The hybrid methodology overcomes smearing, in which purely data-driven approaches isolate affected correlated signals instead of the originating fault.This enables isolation of the root cause rather than all signals deviating from their expected values.Source: §8 · pp. 19–20
  • Hybrid-model advantages are particularly relevant for complex datasets with large operating-condition variability.For more homogeneous operating conditions, similar hybrid and data-driven fault-detection performance is expected.Source: §8 · p. 20
  • Feature-learning analysis links excellent hybrid detection to a latent space z that is informative about the true label class.The latent representation therefore captures discriminative information useful for detection.Source: §8 · p. 20
  • Accurate fault isolation requires a calibrated system model that represents the fault modes.Unrepresented fault modes may reduce isolation capability; residual-based mitigation and realistic validation remain future research topics.Source: §8 · p. 20

9 Appendix I: Neural Network Overview

The appendix reviews discriminative and generative neural networks used for diagnostics, including feed-forward networks, autoencoders, HELM, and VAEs. It explains their mappings, latent representations, reconstruction objectives, probabilistic formulation, and ELBO-based training.

9 Appendix I: Neural Network Overview

  • The appendix covers discriminative models that map inputs to labels and generative models that learn the underlying data distribution.The reviewed architectures include feed-forward networks, vanilla autoencoders, HELM, and variational autoencoders.Source: §9 · p. 22, §9.2 · pp. 23–24

9.1 Discriminative models

  • Feed-forward networks implement parameterized maps from input space R^n to an output space, with weights and biases learned by backpropagation on input-output pairs.Their empirical risk is defined on the training set using a loss function.Source: §9.1 · p. 22
  • Autoencoders use an encoder to compress x into a latent representation z and a decoder to reconstruct x from z, typically through a bottleneck with d < n.Their training objective is reconstruction of the input, making them nonlinear generalizations of PCA.Source: §9.1 · p. 23
  • HELM uses hierarchical hidden representations with random projection parameters and layer-wise optimized weights for reconstruction.Its architecture and training process differ from standard feed-forward and autoencoder networks.Source: §9.1 · p. 23

9.2 Generative models

  • VAEs model x through a stochastic latent variable z using probabilistic encoder qφ(z|x) and decoder pθ(x|z) networks.They assume a prior p(z) and optimize the ELBO, combining expected reconstruction performance with KL regularization toward the prior.Source: §9.2 · p. 24
  • The VAE ELBO combines expected negative reconstruction error with a KL-divergence term that regularizes the approximate posterior toward the prior.Under stated distributional assumptions, the KL term is analytically integrated and the reconstruction expectation is estimated by sampling.Source: §9.2 · p. 24
  • VAE training uses reparameterization to express z as a differentiable transformation of input x and auxiliary noise ε, enabling lower-variance gradient estimation.The encoder outputs the approximate posterior parameters μ and log σ^2 under a diagonal-Gaussian assumption.Source: §9.2 · p. 24
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