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Bayesian thermal digital twin for a space habitat subjected to an impact event

Sreehari Manikkan, Seungho Rhee, Herta Montoya, Davide Ziviani, Shirley J. Dyke, Ilias Bilionis

arXiv:2609.04614v1eess.SYeess.SP

TL;DR

Impact-driven damage can create evolving thermal anomalies in space habitats, while thermal digital-twin capabilities for ECLSS remain limited. The paper develops and validates a Bayesian twin coupling physical and cyber RC models with physics-based adaptation, enabling uncertain anomaly and impact inference. It reports anomaly detection, parameter inference, temperature forecasting, and time-to-critical estimation for autonomous habitat operation.

  • Problem

    Thermal digital twins for ECLSS remain limited despite the need to manage impact-induced, time-evolving habitat anomalies under uncertainty.

  • Method

    The study couples physical and cyber RC thermal models with physics-based activation functions and Bayesian inference for adaptive model selection and health-state estimation.

  • Results

    The validated framework detects thermal anomalies, infers impact location, timing, and severity, forecasts temperatures, and estimates time-to-critical with quantified uncertainty.

  • Takeaways & Limitations

    The digital twin supports uncertainty-aware monitoring and decision-making for impact-driven thermal disruption in autonomous space-habitat operation.

  • Takeaways & Limitations

    The study does not address digital-twin life-cycle management, including long-term operation, aging-related updates, or twin reset after anomaly detection.

Abstract

from arXiv · show

Space habitats may experience disruptive events, such as micro-meteorite impacts, that can induce structural damage and thermal anomalies in the interior environment, requiring resilient Environmental Control and Life Support Systems (ECLSS). Digital twins offer a promising paradigm for supporting resilience, onboard decision making, and uncertainty-aware autonomy. However, limited work has developed digital twins for the thermal aspects of ECLSS. This work develops a Bayesian thermal digital twin for a habitat cyber-physical testbed experiencing impact-induced thermal anomalies. We construct a coupled thermal resistance-capacitance network model representing the physical and cyber thermal subsystems and embed physics-based activation functions to automate model selection, enable adaptation, and facilitate health-state estimation. Offline Bayesian calibration is performed for the physical subsystem using experimental temperature data. For the cyber subsystem, reduction in structural protective layer thickness is identified as the impact-sensitive parameter. After fixing the physical parameters and insensitive parameters, Bayesian inference is performed continuously to estimate impact-relevant cyber parameters, enabling detection of impact location, timing, and severity. Synthetic studies examine hyperparameter selection, observability, and noise effects, and the final framework is validated using experimental testbed data. Results show that the proposed digital twin can detect impact-induced thermal anomalies, infer impact-relevant parameters with quantified uncertainty, generate informative temperature forecasts, and support time-to-critical estimation for autonomous habitat operation.

1. Introduction

The paper targets thermal digital twins for space habitats exposed to impact-induced anomalies, combining Bayesian inference with physics-based adaptation for uncertainty-aware monitoring and decision support.

  • Motivation: Micro-meteorite and orbital-debris impacts can damage habitat structures, alter thermal behavior, and threaten crew safety.Experiments observed time-dependent changes in structural and interior temperatures and thermal-management operation after simulated damage.
  • Research gap: ECLSS digital twins are promising for situational awareness, state estimation, and predictive analytics, but thermal-focused implementations remain limited.Prior work has studied ECLSS fault detection and thermal anomaly detection, yet few efforts address thermal digital twins comprehensively.
  • Research gap: Thermal anomalies evolve over time through altered heat transfer, motivating dynamic models that estimate anomaly severity, predict system evolution, and assess time-to-critical with uncertainty.The paper emphasizes gradual temperature-trend or slope changes caused by compromised insulation and leakage effects.
  • Approach: The proposed Bayesian twin couples physical and cyber RC thermal models and uses physics-based activation functions for model selection, adaptation, and health-state estimation.The activation functions support inference of impact time, location, intensity, and effective insulation reduction without a separate health-state random variable.
  • Approach: The framework calibrates the physical subsystem offline, evaluates synthetic-data trade-offs, and then supports continuous updating on experimental data.The workflow includes posterior calibration, sensitivity and performance studies, verification of continuous updating, and experimental validation.
  • Scope: The paper validates anomaly detection, probabilistic impact inference, temperature forecasting, and time-to-critical estimation through synthetic studies and testbed data.The paper is organized around experimental setup, model construction, Bayesian formulation, calibration, synthetic analyses, validation, and conclusions.

2. Experimental Setup

The study uses HARSH, a cyber-physical lunar-habitat testbed, to develop a thermal digital twin for impact-driven damage to the structural protective layer.

  • Testbed: HARSH is a cyber-physical testbed representing a smart habitat with numerical cyber components and laboratory-realized physical components.The testbed integrates lunar-habitat systems with a health-management system.
  • Testbed: The experimental setup focuses on interior-environment thermal behavior after an impact damages the structural protective layer.The digital twin targets thermal anomaly detection, temperature prediction, and time-to-critical estimation under this disruption scenario.

3. Lumped Parameter Thermal Model

The paper builds a reduced-order coupled RC thermal model for the HARSH testbed, representing physical, transfer, and cyber thermal subsystems. Physics-based activation functions switch between nominal and fault models while linking SPL damage to thermal and health-state behavior.

  • Physical subsystem: The physical subsystem models interior air, bladder surfaces, floor, ceiling, and auxiliary unobserved thermal nodes as lumped masses.Ten side panels plus floor and ceiling define the primary bladder-surface nodes, with additional nodes representing unobserved heat interactions.
  • Physical subsystem: The model observes selected air and surface temperatures while treating alternating panel nodes and auxiliary nodes as unobserved states.External panel temperatures are used as input signals during physical-subsystem Bayesian calibration.
  • Cyber subsystem: The cyber subsystem represents SPL behavior with nine panel-wise boundary-temperature nodes and identifies effective SPL thickness as the impact-sensitive quantity.Panel 10 is excluded from the cyber SPL representation, while SPL thickness and thermal properties determine model parameters.
  • Model construction: The digital twin combines separate physical and cyber thermal models into coupled nominal and fault-condition models.The coupled formulation supports automatic selection between operating conditions.
  • Digital twin model: The Heaviside activation switches from the nominal model before impact to the fault model after impact, enabling automatic model selection and adaptation.The activation uses physics-based constraints on inferred SPL thickness reduction and impact timing.
  • Digital twin model: Physics-based parameter constraints express health state through the inferred parameters, while radiation is activated and strengthened as SPL thickness reduction increases.This avoids a separate health-state random variable and makes the radiation contribution zero without inferred damage.

4. Probabilistic Model Formulation

The probabilistic formulation uses Bayesian inference for both offline physical-model calibration and online estimation of impact-relevant cyber parameters. It combines a deterministic thermal dynamical system with noisy temperature observations to quantify parameter and state uncertainty.

  • Bayesian formulation: Bayesian calibration is used because quantified uncertainty during simulation-model calibration is a key digital-twin requirement.The calibrated physical parameters support subsequent synthetic studies and online inference.
  • Offline and online inference: Offline inference estimates physical-subsystem parameters, whereas online inference fixes selected parameters and estimates SPL thickness reduction and impact time.The online parameter vector includes l_SPL,j, Δl_SPL,j, and t_impact,j for j ∈ {1, 2, ..., 9}.
  • Observation model: The framework assumes known inputs and no latent process noise, while uncertainty is represented through noisy temperature observations.Modeling uncertain inputs or latent process noise would require a stochastic system model beyond the stated scope.
  • Observation model: The observation model uses a measurement mask to select observed states and independent Gaussian noise to generate discrete-time temperature data.The posterior is formed over unknown parameters, initial conditions, and observation-noise variances.
  • Computational formulation: The deterministic state trajectory is computed with a differentiable ODE solver within the Bayesian likelihood formulation.The implementation uses Dormand-Prince’s 5/4 method.

5. Offline Bayesian Calibration of the Physical Subsystem Model

Offline Bayesian calibration estimates the physical subsystem’s thermal-model parameters from experimental temperature data and evaluates predictive behavior beyond the calibration regime. The calibrated model reproduces measured thermal dynamics, while predictions for unobserved states remain physically plausible but cannot be independently verified.

  • Model and data: The physical subsystem model contains 17 states, 9 observed states, and 98 estimated parameters.The parameters comprise 72 dimensionless model parameters, 17 initial-condition parameters, and 9 observation-noise parameters.
  • Model and data: The calibration dataset uses cryogenic-chiller-conditioned heat-transfer fluid and is designed to span informative operating behavior with minimal measurement noise.The study emphasizes operating-range coverage and input excitation for parameter identification.
  • Model and data: 42101 measurements were recorded at 1 s intervals, then subsampled, trimmed by 100 initial points, and normalized to [-1,1].The preprocessing removes initial abrupt fluctuations and obtains uniform initial conditions.
  • Model and data: The evaluation regime includes an upward trend from trough to crest that is not fully present during calibration, testing prediction beyond the training behavior.This distinct trend assesses whether the calibrated model predicts system dynamics outside the calibration data.
  • Bayesian calibration: Variational inference with a block neural autoregressive flow ran for 10000 iterations until the loss showed minimal variation.The guide was implemented with NumPyro, and the stabilized loss was used to indicate a good posterior approximation.
  • Calibration results: 95% credible intervals contain training measurements, and predictions at unseen time instants align very well with measurements.Unobserved-state trajectories are qualitatively physically plausible, but their accuracy cannot be independently verified without corresponding measurements.
  • Calibration results: Successful offline calibration supports proceeding to synthetic trade-off studies for controlled impact scenarios and online-inference settings.The calibrated physical model is treated as sufficiently accurate for subsequent digital-twin analyses.

6. Synthetic Examples with Trade-off Studies

The synthetic studies evaluate continuous Bayesian updating for thermal health-state inference, temperature prediction, and time-to-critical estimation under batch-size, observability, and noise trade-offs. Results identify a preferred batch-size setting, quantify observability limits, and show how post-impact data availability affects detection reliability.

  • Continuous Bayesian Updating: The digital twin updates parameters sequentially using batches whose sizes increase from BSmin to NBSBSmin before remaining fixed.For inference j, BSj = j · BSmin through NBS, then BSj = NBSBSmin.
  • Batch-Size Hyperparameter Study: 100% configuration accuracy is achieved throughout the inference sequence by (2, 3) and all combinations with BSmin = 3 before impact.These configurations show perfect agreement between the highest-posterior-probability health-state configuration and the true configuration.
  • Batch-Size Hyperparameter Study: The (2, 5) combination produces a false-positive detection at the impact time, so corresponding first-detection and TTC estimates are not reported.After impact, successful detection persists only while batches contain sufficient pre- and post-impact temperature variation; updating becomes unreliable with post-impact-only data.
  • Batch-Size Hyperparameter Study: The (3, 4) batch-size combination provides the best overall trade-off, maintaining 100% configuration accuracy and posterior probability above 0.5 except at the final inference.Its computational time remains relatively low after impact, and its subsequent TTC estimates remain reasonably large and non-zero.
  • Observability Analysis: Reduced observability progressively degrades damage localization: level 1 retains 100% accuracy, levels 2 and 3 detect successfully at inference 6, and level 4 achieves no successful detection.Level 1 observes all damaged-panel interior temperatures, whereas level 4 observes only TIE.

7. Experimental Validation

Experimental validation shows that the digital twin detects impact-induced thermal anomalies, updates impact-relevant parameters, predicts temperatures, and estimates time to critical conditions with quantified uncertainty.

  • An impact damaging panels 7, 8, and 9 at 4408 s caused an 87.5% reduction in structural protective layer thickness.
  • The digital twin maintained posterior health-state probability within [0.5,1], while execution times ranged from 2 to 7 minutes for nominal and anomaly-detection inferences.
  • Because panel 8 was unobserved, the successful detection identified damage on panels 7 and 9 but not panel 8.
  • Posterior parameter distributions remained near their priors before impact information entered the training window, then concentrated near true values from inference 7.
  • The first TTC estimate underestimated the true value, whereas subsequent credible intervals contained the true TTC values and became narrower.
  • Offline-calibrated quantities and parameters c1, c2, and c3 were represented as point estimates rather than jointly inferred online.

8. Conclusions

The framework supports thermal anomaly detection, temperature prediction, and TTC estimation for impact-driven disruptions, but its scope excludes several digital-twin life-cycle functions needed for sustained autonomy.

  • The Bayesian thermal digital twin detects thermal anomalies, predicts temperatures, and estimates TTC for an extraterrestrial habitat testbed experiencing SPL impact damage.
  • The work does not address long-term operation, updates after aging or major system changes, or twin resetting and reinitialization after anomaly detection.
  • Future work targets more computationally efficient Bayesian inference and a coupled temperature, pressure, and air-concentration health model.

CRediT authorship contribution statement

The contribution statement assigns conceptualization, methodology, investigation, software, validation, visualization, and writing roles across the listed authors.

  • Sreehari Manikkan contributed conceptualization, methodology, investigation, software, validation, visualization, and original-draft writing.
  • Seungho Rhee, Herta Montoya, Davide Ziviani, Shirley J. Dyke, and Ilias Bilionis are credited with combinations of data curation, investigation, supervision, funding acquisition, and manuscript review.

Data availability

The paper states that datasets will be made publicly available after acceptance and discloses the use of ChatGPT for language correction.

  • Datasets will be made publicly available once the paper has been accepted for publication.
  • The authors used ChatGPT to correct spelling, grammatical, and syntactical errors, then reviewed and edited the content.

Appendix A Sensitivity Analysis

The sensitivity analysis distinguishes parameters governing baseline thermal dynamics from those governing impact-induced changes. Fixing c1, c2, and c3 makes the impact-relevant parameters more interpretable for online inference.

  • Analysis setup: The analysis fixes timpact,j at 4000 s to isolate sensitivity structure in the pre-impact and post-impact regimes.Parameter ranges are specified for c1, c2, c3, lSPL,j, and ΔlSPL,j.
  • Joint sensitivity analysis: With all parameters varied, c1 dominates the response before impact and remains more influential than ΔlSPL,j after impact.Its first-order and total-order indices are nearly identical and close to unity before impact.
  • Fixed-parameter sensitivity analysis: With c1 = 0.025, c2 = 1, and c3 = 0.1 fixed, lSPL,j dominates before impact and ΔlSPL,j dominates after impact.The close first-order and total-order indices indicate largely direct effects rather than interaction-driven effects.

Appendix B Synthetic Example Plots

The synthetic-study plots report posterior temperature predictions, posterior impact-time and thickness-reduction distributions, and estimated observation-noise levels. Figure 13 separately displays Sobol sensitivity indices under two parameter-variation settings.

  • Sensitivity plots: Figure 13 plots state-averaged first-order S1 and total-order ST Sobol indices over time for synthetic impact data.
  • Temperature predictions: Figure 14 shows posterior predictive distributions of observed temperatures across inferences for the (BSmin, NBS) = (3, 4) combination.The grey-shaded region marks the data used for Bayesian inference.
  • Impact-time inference: Figure 15 shows posterior distributions of impact-time parameters timpact,j across inferences for the (BSmin, NBS) = (3, 4) combination.
  • Thickness-reduction inference: Figure 16 shows posterior distributions of effective-thickness-reduction parameters ΔlSPL,j across inferences for the (BSmin, NBS) = (3, 4) combination.
  • Noise study: Figure 17 reports estimated observation-noise levels across inferences for level 1 observability as 95% posterior credible intervals.The intervals are shown for different imposed observation-noise levels.

Appendix C Experimental Validation Plots

The experimental validation plots present posterior temperature predictions, impact-time and thickness-reduction distributions, and estimated observation-noise levels across inferences. Together, they organize the validation results around forecasts, parameter estimates, and uncertainty.

  • Temperature predictions: Figure 18 shows posterior predictive distributions of observed temperatures across inferences for the experimental validation case.The grey-shaded region marks the data used for Bayesian inference.
  • Impact-time inference: Figure 19 shows posterior distributions of impact-time parameters timpact,j across inferences for the experimental validation case.
  • Thickness-reduction inference: Figure 20 shows posterior distributions of effective-thickness-reduction parameters ΔlSPL,j across inferences for the experimental validation case.
  • Noise estimates: Figure 21 reports estimated observation-noise levels across inferences for the experimental validation case as 95% posterior credible intervals.
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