PaperlayerView exact revision on arXiv

Source-linked AI summary

Sensor Fault Detection, Isolation and Identification Using Multiple Model-based Hybrid Kalman Filter for Gas Turbine Engines

Bahareh Pourbabaee, Nader Meskin, Khashayar Khorasani

arXiv:1505.02063v2eess.SY

TL;DR

Gas-turbine FDII must detect, isolate, and estimate sensor faults despite changing operating conditions and health-parameter degradation. The paper proposes a hierarchical multiple-HKF scheme that combines an OBEM with PWL models, Bayesian interpolation, and modified GLR estimation. Simulations report prompt detection and isolation, lower false alarms, and robustness to health-parameter degradation relative to alternative filtering schemes.

  • Problem

    Gas-turbine FDII must distinguish sensor faults from false-alarm effects caused by engine aging and uncertain health-parameter degradation.

  • Method

    The paper combines a nonlinear OBEM with PWL models in a hierarchical multiple-HKF structure, using Bayesian interpolation for operating-regime coverage and modified GLR for fault-severity estimation.

  • Results

    The proposed MHKF-based FDI scheme promptly detects and isolates sensor-bias faults across the flight profile, with improved robustness and fewer false alarms than compared approaches.

  • Takeaways & Limitations

    The scheme supports sensor FDII across the engine flight profile and can operate through the engine life cycle by updating health-parameter reference baselines.

  • Takeaways & Limitations

    The derivation relies on an assumption that nominal and updated OBEM linearizations produce approximately the same matrices and steady-state values.

Abstract

from arXiv · show

In this paper, a novel sensor fault detection, isolation and identification (FDII) strategy is proposed by using the multiple model (MM) approach. The scheme is based on multiple hybrid Kalman filters (HKF) which represents an integration of a nonlinear mathematical model of the system with a number of piecewise linear (PWL) models. The proposed fault detection and isolation (FDI) scheme is capable of detecting and isolating sensor faults during the entire operational regime of the system by interpolating the PWL models using a Bayesian approach. Moreover, the proposed multiple HKF-based FDI scheme is extended to identify the magnitude of a sensor fault by using a modified generalized likelihood ratio (GLR) method which relies on the healthy operational mode of the system. To illustrate the capabilities of our proposed FDII methodology, extensive simulation studies are conducted for a nonlinear gas turbine engine. Various single and concurrent sensor fault scenarios are considered to demonstrate the effectiveness of our proposed on-line hierarchical multiple HKF-based FDII scheme under different flight modes. Finally, our proposed HKF-based FDI approach is compared with various filtering methods such as the linear, extended, unscented and cubature Kalman filters (LKF, EKF, UKF and CKF, respectively) corresponding to both interacting and non-interacting multiple model (MM) based schemes. Our comparative studies confirm the superiority of our proposed HKF method in terms of promptness of the fault detection, lower false alarm rates, as well as robustness with respect to the engine health parameters degradations.

I. INTRODUCTION

The paper develops a hierarchical multiple-model FDII strategy for gas-turbine sensor faults across operating regimes, addressing false alarms from engine-health degradation and modeling uncertainty. It combines hybrid Kalman filtering, Bayesian model interpolation, and modified GLR-based fault-severity estimation.

  • Motivation: FDII generates fault residuals, isolates faulty actuators, sensors, or components, and estimates fault severity.The paper frames these as the principal stages of an FDII solution.
  • Proposed approach: The proposed hierarchical non-interacting MM-based HKF structure detects and isolates single and concurrent sensor faults throughout the engine flight profile.The scheme is intended to operate across the engine life cycle by periodically updating health-parameter reference baselines.
  • Proposed approach: Multiple HKFs integrate one nonlinear OBEM with PWL models, while Bayesian interpolation covers the full engine operating regime.The operating range is decomposed into sub-regions represented by PWL models.
  • Fault identification: A modified GLR method estimates sensor-fault severity using the healthy operational mode.The estimated severity can support sensor-measurement reconstruction or removal of a faulty sensor from the measurement set.
  • Motivation: Engine aging effects, including compressor fouling and turbine erosion, can shift health parameters from healthy baselines and produce false alarms.These effects are treated as modeling uncertainty that is difficult to represent in a structured form.
  • Evaluation: The study compares the proposed MHKF-based FDI scheme with LKF-, EKF-, UKF-, and CKF-based MM schemes across detection, false alarms, robustness, and computational time.The paper also formally derives the discrete-time HKF and evaluates the method through simulation scenarios.

III. PIECEWISE LINEAR MODELS (PWL) INTERPOLATION

The interpolation scheme extends local PWL models across the engine operating range by replacing fixed operating-point values with OBEM states and outputs and weighting models probabilistically.

  • PWL model construction: The full operating range is divided into sub-regions, each represented by a PWL model around an operating point.The PWL models are integrated to construct a parameter-varying model for the nonlinear engine.
  • PWL model construction: Replacing steady-state values with OBEM variables extends each PWL model’s valid range beyond its local operating-point neighborhood.The OBEM state and output variables change with engine operating conditions.
  • Sensor modes: The faulty-engine model injects sensor bias faults through fault-location vectors and a step function at each fault occurrence time.There are q+1 sensor modes: one healthy mode and q faulty-sensor modes.
  • HKF construction: State-space and Kalman-gain matrices are stored in look-up tables to construct HKFs for every operating point and sensor mode.The matrices depend on operating points, while Kalman gains also depend on shared noise covariance matrices.
  • Bayesian interpolation: Residuals and covariance matrices from multiple HKFs produce likelihoods whose normalized weights are recursively updated with Bayes’ formula.A lower-bound design parameter prevents low-weight PWL models from being removed and improves numerical robustness.
  • Bayesian interpolation: The weighted PWL matrices, innovations, and covariances form time-varying models operating across the entire engine regime.These weighted quantities are passed to the subsequent FDII stages.

IV. SENSOR FDI VIA MULTIPLE-MODEL-BASED SCHEME

The proposed MM-based FDI scheme uses multiple HKFs associated with sensor modes and operating regions, combining their weighted innovations and covariances across the engine regime.

  • Multiple-model structure: At each operating point, one healthy and q faulty-sensor PWL models are integrated with a single OBEM to form the MHKF scheme.The resulting models represent alternative sensor-health hypotheses.
  • System architecture: Figure 1 depicts the MM-based FDI scheme based on HKFs corresponding to multiple operating regimes.The figure summarizes the architecture rather than reporting a numerical result.

A. Single Fault Detection and Isolation (FDI) Scheme

The single-fault FDI scheme evaluates conditional probabilities for sensor modes and identifies the most probable healthy or faulty-sensor hypothesis from measurement history.

  • Mode probabilities: The MM scheme defines each sensor-mode probability as the conditional probability that the fault parameter assumes that mode given measurements through time k.The probabilities are conditioned on the observed measurement history.
  • Mode probabilities: The current measurement likelihood for each sensor mode is computed using a Gaussian density function.The likelihood is based on the mode-specific innovation and covariance quantities.
  • Detection and isolation: The correct sensor mode tends to receive the largest probability because its innovation and covariance determinant are smaller than those of mismatched filters.Fault detection and isolation follow by evaluating the mode probabilities and selecting their maximum.
  • Detection and isolation: The method generalizes an earlier single-operating-point linear-MM structure to the entire engine regime using multiple HKFs and fused innovations and covariances.This modification targets operation across varying engine conditions.
  • Sensor modes: The single-fault setup defines six modes: one healthy mode and five modes for 3% bias faults in specified engine sensors.The faulty sensors include compressor-exit temperature and pressure, shaft speed, and turbine-exit temperature and pressure.
  • Concurrent faults: Table I lists operational modes corresponding to possible pairs of concurrent sensor faults.Its caption identifies the table as a mapping of operational modes for two concurrent faults.

B. Concurrent Fault Detection and Isolation (FDI) Scheme

The hierarchical non-interacting multiple-model scheme detects and isolates concurrent sensor faults sequentially, then estimates their severity using a modified GLR method.

  • Concurrent fault detection and isolation: The first filter level monitors healthy sensors and five single-fault modes, while later levels detect and isolate additional concurrent faults.The scheme activates the second filter level after the first fault is detected and isolated.
  • Concurrent fault detection and isolation: Concurrent faults are assumed not to occur simultaneously; a minimum interval separates their occurrences.
  • Concurrent fault detection and isolation: The MM-based FDI scheme uses predetermined sensor-bias severity values shared across filters and currently represents one fault-severity level.Additional severity levels can be incorporated by increasing the number of filters.
  • Fault severity identification: After fault time and location are determined by the MHKF scheme, the modified GLR estimates severity using the healthy-mode residuals.The GLR detection stage is removed because occurrence time and location are already known.
  • Fault severity identification: The modified GLR produces a minimum-variance unbiased estimate of the sensor-bias fault magnitude and can also estimate multiple previously isolated concurrent faults.
  • Fault severity identification: The fault-identification module does not feed severity estimates back into the FDI scheme, which otherwise would require variable-structure filter updates.

VI. SIMULATION RESULTS

Simulations evaluate the proposed FDII scheme on a nonlinear single-spool jet-engine model across climbing, cruise, and landing conditions, using multiple operating-point models and sensor modes.

  • Simulation setup: The simulations use a nonlinear single-spool jet-engine model with process and measurement noise, while health-reference baselines are periodically updated by offline monitoring.
  • Simulation setup: The engine model contains four state variables, one fuel-flow actuator, five sensor outputs, and four health parameters describing compressor and turbine performance.
  • Simulation setup: The flight condition is represented by altitude and Mach number, with ambient temperature and pressure computed from environmental conditions.
  • Simulation setup: The system is simulated for 520 sec at a 0.01-sec sampling rate, using flight-profile inputs whose altitude, Mach number, and fuel-flow profiles are shown in Fig. 2.
  • FDII configuration: Six PWL-model sets represent five faulty sensor modes and one healthy mode, with predetermined bias faults equal to 3% of cruise steady-state outputs.
  • FDII configuration: Five operating points cover the climbing, cruise, and landing modes, with two points assigned to each variable-input phase and one to cruise.
  • FDII configuration: Sensor faults are detected and isolated by selecting the mode with the maximum generated probability.

A. Case 1: False Alarms Evaluation

The false-alarm evaluation tests the FDII scheme under mismatches between actual and estimated engine health-reference baselines during the full flight profile.

  • False-alarm sources: Dynamic model mismatch, offline health-monitoring errors, and process or measurement noise are identified as potential sources of false alarms.
  • Robustness evaluation: The evaluation investigates robustness to reference-baseline estimation error, defined from the absolute difference between actual and estimated health baselines.
  • Robustness evaluation: 3% compressor and 2% turbine health-parameter baseline estimation errors are the maximum levels reported without false alarms in healthy-sensor simulations.
  • Robustness evaluation: Beyond those error limits, false alarms may increase; within them, healthy-mode probability remains near one and faulty-mode probabilities remain almost zero throughout the flight profile.
  • Robustness evaluation: Fig. 3 shows mode probabilities for 3% bias faults applied to TC, PC, and N sensors at 50, 250, and 450 sec, respectively.

B. Case 2: A 3% Sensor Bias Fault Detection and Isolation

The proposed sensor FDI scheme is evaluated for a 3% bias fault across the complete flight profile and under health-parameter and measurement-noise uncertainties. Fault detection remains possible across flight modes, while increasing uncertainty delays detection and degrades classification metrics.

  • Experimental setup: The evaluation applies a 3% sensor bias fault during a 520-second flight profile and assesses detection time against reference-baseline estimation error.The fault occurs under cruise-condition steady-state output scaling, while the analysis spans the entire flight profile.
  • Fault detection across flight modes: Fault detection is faster during cruise than during climbing or landing, but remains possible despite larger thrust and ambient-condition variations.Cruise has less variation in thrust and ambient conditions than the other flight modes.
  • Robustness evaluation: Confusion matrices evaluate fault isolation under compressor and turbine health-parameter degradations, with rows representing fault conditions and columns representing isolated faults.Each matrix element CMij is the rate at which fault j is isolated when fault i occurs.
  • Robustness evaluation: Measurement noise is separately tested by multiplying the original sensor-noise standard deviations by a factor of 20.This test examines the effect of strong measurement-noise signals on the FDI scheme.
  • Uncertainty effects: Increasing reference-baseline estimation error or measurement-noise uncertainty delays detection and increases false alarms and incorrect fault detections.The corresponding performance indices are false positive rate, accuracy, and incorrect fault detection rate.
  • Uncertainty effects: Higher uncertainty decreases accuracy while increasing false positive and incorrect fault detection rates, although the scheme remains sufficiently robust at high uncertainty levels.The reported uncertainty sources include measurement noise and discrepancies between the OBEM and actual engine health parameters.

C. Case 3: Sensor Fault Detection and Isolation for Different Fault Severities

The study examines sensor-bias detection and isolation when actual fault severities differ from the 3% bias used to design the multiple-model structure. Detection is possible within a bounded severity range, but faults beyond the maximum detectable magnitude can produce incorrect isolation.

  • Fault-severity dependence: The minimum detectable sensor bias is 2%, and it requires longer detection times than higher severities, especially during climbing and landing.The analysis uses faults occurring at different flight-profile stages under maximum tolerable compressor-health-parameter baseline errors.
  • Operational range: The multiple-model structure is designed for a 3% sensor bias fault, so its detection and isolation capability is bounded by the severity range represented by its models.The paper reports maximum detectable severities under compressor and turbine health-parameter baseline-error limits.
  • Operational range: Applying a bias beyond the corresponding maximum detectable severity can lead to an incorrect fault detection.The reported maximum severities are averaged over all flight modes and incorporate the stated health-parameter error limits.
  • Extension: The authors recommend adding multiple-model components for higher predetermined sensor faults to detect and isolate larger magnitudes more quickly.The recommendation directly addresses faults exceeding the current detectable range.

D. Case 4: Sensor Fault Severity Identification

The proposed framework supplements multiple-model fault-level information with a modified GLR method to estimate sensor-bias magnitude. Within the scheme’s operational range, the resulting reconstructed outputs show low weighted mean square normalized error.

  • Severity-identification method: The modified GLR method estimates sensor-bias fault magnitude and severity because the multiple-model scheme alone provides only fault-level information, not exact severity.The estimated magnitude is integrated into the FDII framework after fault detection.
  • Severity-identification method: Equation (23) constructs numerical outputs using the estimated fault magnitude and detected fault-occurrence time for each fault-associated operational mode.The construction uses the estimated state, OBEM output, and fault-vector effect without feeding the estimate back to update filter bias models.
  • Results: Average WMSNE remains below 0.5% for various faults within the FDI scheme’s operational range.This result is reported across the tested fault cases and flight modes without health-baseline estimation error.

E. Case 5: Concurrent Fault Detection, Isolation and Identification

The hierarchical FDII scheme is tested on concurrent sensor faults occurring at different flight-profile stages. In the reported scenarios, the faults are detected and isolated within seconds, with low reconstructed-output error.

  • Concurrent-fault evaluation: The hierarchical scheme diagnoses concurrent sensor faults occurring at different stages of the flight profile.The case study reports detection and isolation times together with WMSNE values for two selected scenarios.
  • Scenario results: In the first scenario, concurrent faults are detected after 1.7 and 2.4 seconds and isolated after the corresponding events, with WMSNE values of 0.0208% and 0.106%.These values are reported for the two concurrent faults in that scenario.
  • Scenario results: In the second scenario, 4% and 6% bias faults are detected after 0.9 and 0.4 seconds, respectively, with WMSNE values of 0.0125% and 0.1702%.The faults affect the TT sensor during cruise and the PT sensor during landing.

F. Case 6: Comparison

The comparison evaluates MHKF-based FDI against alternative filters under healthy and degraded engine conditions, including non-interacting and interacting MM structures. MHKF detects faults promptly, remains robust to health-parameter degradation, and uses fewer operating points than MLKF.

  • Comparison setup: The MHKF-based FDI scheme is compared with LKF, EKF, UKF, and CKF approaches using common noise settings and MM residual structures.The experiments assess detection, isolation, robustness to health degradation, and computational requirements.
  • Non-interacting MM comparison: All filters detect and isolate a 3% single sensor bias fault during cruise, but MHKF detects it faster than the alternatives.The fault is injected at kf = 250 sec without health-parameter degradation.
  • Robustness to degradation: With 2.5% compressor health-parameter degradation, MHKF avoids false alarms before the fault, whereas EKF and MLKF generate false alarms.The scenario applies a 3% TC-sensor bias fault while the OBEM health parameters remain unupdated.
  • Interacting MM comparison: Interactions among models do not improve MHKF-based FDI, and IMM use is not recommended unless off-diagonal transition probabilities remain below 0.001.Otherwise, the healthy-mode probability can fall to almost 0.8 before a fault, increasing false-alarm risk.
  • Operating-point and resource comparison: MHKF has an implementation memory disadvantage because it stores look-up tables, although the required number of operating points is smaller than for MLKF.Using stored steady-state gains, MLKF averages about 80 seconds, less than MHKF in that comparison.
  • Operating-point and resource comparison: MHKF requires fewer operating points than MLKF because five points cover the flight profile while MLKF cannot track rapid thrust variations during climbing and landing.MLKF therefore needs more points and can produce false alarms from higher estimation error.

VII. CONCLUSIONS

The paper concludes that hierarchical multiple-HKF FDII integrates nonlinear engine modeling with PWL estimators to diagnose single and concurrent sensor faults across the flight envelope. It incorporates health-parameter updates and modified GLR severity estimation, with simulations reporting stronger robustness and accuracy than competing filters.

  • Conclusions: The proposed hierarchical MM-based FDII method detects, isolates, and identifies single and concurrent sensor faults in gas turbine engines.The approach uses HKF detection filters within a hierarchical multiple-model structure.
  • Conclusions: HKF integrates a nonlinear OBEM with PWL models so linear filters can represent engine nonlinearities across the operating range.Compared with MLKF, the approach uses fewer operating points, each covering a larger operating range.
  • Conclusions: Updating OBEM health-parameter reference baselines incorporates engine degradation effects and helps prevent false alarms and incorrect fault detections.This design supports operation across the flight profile and engine life cycle.
  • Conclusions: The MM-based FDI scheme is integrated with a modified GLR method to estimate sensor fault severity.The conclusion identifies severity estimation as an extension of the proposed FDII framework.
  • Conclusions: Simulation studies report that MHKF-based FDI has superior accuracy and robustness to health-parameter degradation compared with MLKF, EKF, UKF, and CKF.The HKF formulation relies on linearized and discretized OBEM models, with higher-order terms and approximation error neglected under the stated assumption.
Loading 1505.02063v2…