Degradation-model-based state-of-health estimation algorithms are critical for assessing battery performance over time. These algorithms rely on electrochemical models to quantify capacity fade, power loss, and aging mechanisms. The accuracy of these models directly impacts battery management, lifetime prediction, and safety in applications ranging from electric vehicles to grid storage. Three primary techniques dominate model-based SOH estimation: differential voltage analysis, incremental capacity analysis, and impedance-based health indicators. Each method provides unique insights into degradation pathways while differing in computational complexity and measurement requirements.

Differential voltage analysis examines the voltage curve's derivative during charge or discharge. The peaks and valleys in the differential voltage curve correspond to phase transitions in electrode materials. As batteries age, these features shift due to loss of active material, lithium inventory, or electrode kinetic degradation. For lithium-ion batteries with graphite anodes, the peak near 3.4V versus lithium reflects staging transitions in graphite. The magnitude and position of this peak correlate with anode degradation. Similarly, the plateau region in the differential voltage curve for lithium iron phosphate batteries indicates phase separation in the cathode. Tracking these features over cycles provides quantitative SOH metrics without requiring full discharge cycles. The method's sensitivity to electrode-specific degradation makes it valuable for diagnosing aging mechanisms.

Incremental capacity analysis complements differential voltage analysis by evaluating capacity changes per unit voltage. The incremental capacity curve's peak height and area relate to active material availability and lithium-ion diffusion properties. In nickel-manganese-cobalt cathodes, the reduction in peak height at 3.7V indicates loss of accessible lithium, while peak broadening suggests increased polarization resistance. This technique excels at identifying nonlinear aging effects, such as when capacity fade accelerates after certain cycle counts. The resolution of incremental capacity analysis depends on the voltage measurement precision, with errors below 1 mV preferred for reliable feature extraction. Both differential voltage and incremental capacity methods require controlled low-current conditions to minimize polarization effects that obscure degradation signatures.

Impedance-based health indicators track changes in the battery's internal resistance and charge transfer kinetics. Electrochemical impedance spectroscopy decomposes the total impedance into ohmic resistance, charge transfer resistance, and Warburg diffusion elements. The rise in charge transfer resistance at the anode-electrolyte interface often precedes measurable capacity loss, providing early warning of degradation. For high-power applications, the increase in ohmic resistance directly impacts power capability independent of capacity fade. Multi-frequency impedance measurements can isolate degradation in specific components, such as separator aging from electrode cracking. However, impedance-based methods require specialized instrumentation and are sensitive to temperature and state-of-charge variations that must be compensated in the analysis.

Model-based SOH estimation contrasts with data-driven approaches in several key aspects. Physics-based models incorporate known electrochemical relationships, such as the Butler-Volmer equation for charge transfer or Fick's laws for diffusion. These models provide interpretable parameters like solid-phase diffusion coefficients or reaction rate constants that directly link to material degradation. The Doyle-Fuller-Newman model, for example, can predict capacity fade from porosity changes in the electrodes. Such models require fewer training data than machine learning methods but depend on accurate parameterization of the battery's initial state. Their computational intensity often limits real-time implementation without simplifications.

Data-driven methods bypass physical modeling by learning patterns from operational data. Neural networks and support vector machines correlate features like charge time, temperature, and voltage profiles with measured capacity fade. While these approaches adapt well to complex aging patterns, they demand large datasets covering diverse operating conditions. Hybrid methods are emerging that combine model-based feature extraction with data-driven regression. For instance, differential voltage peaks might serve as inputs to a Gaussian process model that predicts remaining useful life. This fusion leverages physical interpretability while accommodating nonlinear aging behaviors not fully captured by first-principles models.

The choice between model-based and data-driven SOH estimation involves tradeoffs. Model-based methods excel when degradation mechanisms are well-understood and consistent across cells, as in standardized battery designs. They provide actionable diagnostics, such as identifying whether capacity loss stems from anode or cathode degradation. Data-driven approaches adapt better to heterogeneous battery populations or novel chemistries where physics models are incomplete. Both face challenges in extrapolating beyond their training domains, whether in cycle life or operating conditions.

Validation of SOH algorithms requires correlation with direct capacity measurements under controlled aging conditions. Accelerated aging tests at elevated temperatures or high charge rates help build degradation models but must account for potential changes in failure modes compared to real-world operation. The most robust implementations combine multiple health indicators, such as using impedance trends to cross-validate differential voltage analysis results. This multi-modal approach reduces false degradation alarms from any single metric.

Future advancements in degradation modeling will integrate more detailed descriptions of material evolution, such as particle cracking or solid-electrolyte interphase growth. Coupling these micro-scale models with cell-level performance predictions remains computationally challenging but could enable earlier and more precise SOH estimation. The development remains constrained by the need for destructive physical analysis to validate model predictions against actual material states. Non-destructive techniques like X-ray diffraction or neutron imaging, when combined with model-based interpretation, may bridge this gap.

The effectiveness of any SOH algorithm ultimately depends on its integration with battery usage patterns. Algorithms optimized for electric vehicle cycling may perform poorly in grid storage applications with different depth-of-discharge profiles and idle periods. Customizing degradation models for specific operational contexts remains an active research area, particularly for emerging chemistries like solid-state or lithium-sulfur batteries where aging mechanisms differ fundamentally from conventional lithium-ion systems. The translation of laboratory-scale degradation understanding to field conditions continues to challenge both model-based and data-driven approaches.