Uncertainty quantification (UQ) plays a critical role in the development and validation of degradation models for batteries, particularly in mission-critical applications such as aerospace systems. These models predict how battery performance declines over time due to factors like cycling, temperature fluctuations, and mechanical stress. However, predictions are inherently uncertain due to variability in materials, manufacturing processes, and operating conditions. UQ methods provide a systematic approach to quantify and manage these uncertainties, ensuring that degradation models are both accurate and reliable.

Sensitivity analysis is a foundational UQ method used to identify which input parameters contribute most to uncertainty in degradation predictions. By varying model inputs within plausible ranges, sensitivity analysis ranks parameters based on their influence on outputs such as capacity fade or impedance growth. For example, in lithium-ion batteries, the degradation rate may be highly sensitive to temperature and charge/discharge rates but less sensitive to minor variations in electrode thickness. Local sensitivity methods, such as one-factor-at-a-time (OFAT) analysis, are simple but limited in capturing interactions between variables. Global sensitivity techniques, like Sobol indices or Morris screening, provide a more comprehensive assessment by exploring the entire input space. These methods help engineers prioritize which parameters require tighter control during manufacturing or operation to minimize performance variability.

Bayesian inference is another powerful UQ tool for refining degradation models using observed data. Unlike traditional frequentist approaches, Bayesian methods treat model parameters as probability distributions rather than fixed values. Starting with a prior distribution based on historical data or expert knowledge, Bayesian updating incorporates new experimental or field data to produce a posterior distribution that reflects reduced uncertainty. For instance, a Bayesian framework can update the degradation rate of a battery as real-world cycling data becomes available, improving prediction accuracy over time. Markov Chain Monte Carlo (MCMC) sampling is often employed to approximate posterior distributions when analytical solutions are intractable. Hierarchical Bayesian models further extend this approach by accounting for variability across different battery batches or operating conditions, making them particularly useful for aerospace applications where batteries must perform reliably under diverse scenarios.

Confidence interval estimation complements sensitivity analysis and Bayesian inference by quantifying the range within which a degradation metric is expected to lie with a specified probability. For example, a 95% confidence interval for remaining useful life (RUL) provides bounds that account for both model uncertainty and measurement noise. Methods like bootstrapping generate confidence intervals by resampling available data, while analytical approaches rely on assumptions about the underlying statistical distributions. In aerospace systems, where safety margins are stringent, narrow confidence intervals are essential to avoid overly conservative or risky operational decisions. Advanced techniques, such as polynomial chaos expansion or Gaussian process regression, can also propagate input uncertainties through complex degradation models to produce probabilistic outputs.

The integration of these UQ methods significantly enhances the reliability of degradation models in mission-critical applications. Aerospace systems, for instance, demand batteries that can withstand extreme environments while maintaining predictable performance. A degradation model without UQ might predict a battery’s RUL as a single value, ignoring the risk of premature failure due to unaccounted uncertainties. By contrast, a UQ-informed model provides a probabilistic RUL estimate, enabling operators to make informed decisions about maintenance or replacement. For example, if the model indicates a 10% probability of failure before the next scheduled inspection, preemptive actions can be taken to mitigate risk.

UQ also supports robust design optimization, where degradation models guide the selection of battery materials, architectures, and operating protocols to minimize performance variability. By quantifying how uncertainties propagate to critical outputs, engineers can identify designs that are less sensitive to perturbations. In aerospace applications, this might involve choosing electrode materials with lower degradation rate variability or implementing thermal management strategies that reduce temperature-induced uncertainty. Multi-objective optimization frameworks can balance competing priorities, such as energy density and reliability, while explicitly accounting for uncertainty.

Furthermore, UQ facilitates adaptive management strategies in operational settings. For instance, a satellite’s battery management system (BMS) can use real-time data to update degradation predictions and adjust charging protocols accordingly. Bayesian methods enable continuous learning, where each charge-discharge cycle refines the model’s accuracy. Sensitivity analysis helps prioritize which sensor measurements (e.g., temperature, voltage) are most critical for monitoring, ensuring efficient use of limited onboard computational resources. Confidence intervals provide actionable insights, such as the probability of reaching end-of-life criteria before the next ground station contact, enabling proactive measures.

Despite its advantages, implementing UQ in degradation models presents challenges. Computational cost is a primary concern, particularly for high-fidelity models with numerous uncertain parameters. Surrogate modeling techniques, such as reduced-order models or machine learning emulators, can alleviate this burden by approximating complex simulations with minimal loss of accuracy. Data scarcity is another issue, especially for novel battery chemistries or extreme operating conditions. Here, transfer learning or physics-informed Bayesian priors can leverage knowledge from related systems to compensate for limited direct observations.

In summary, uncertainty quantification transforms degradation modeling from a deterministic exercise into a probabilistic framework that acknowledges and manages real-world variability. Sensitivity analysis identifies key sources of uncertainty, Bayesian inference updates models with empirical data, and confidence interval estimation provides actionable risk metrics. For aerospace and other mission-critical applications, these methods are indispensable in ensuring that batteries meet stringent reliability requirements. By embracing UQ, engineers can design more resilient systems, optimize maintenance schedules, and ultimately extend the safe operational life of energy storage solutions. The continued advancement of UQ techniques, coupled with increasing computational power and data availability, promises further improvements in the accuracy and utility of degradation models across the battery industry.