If the battery life depends only on factors like temperature, Depth of discharge and Charge rate, how can we predict the battery life for varying load pattern( Say for a series of C rates over time )
There are indeed more parameters which affect the battery lifetime such as state of charge (SOC) as well as the battery storage conditions (mostly affect calendar aging).
There are several models, generally categorized under empirical models and physics-based (or electrochemical) models to predict the battery life. The current battery management systems include some levels of fault diagnosis and battery aging prediction depending on the model they use.
There are also some standard experimental testing cycles that can give us some estimate about the degradation of the battery.
The following papers are recommended to get more info:
Article A Heuristic Supervisory Controller for a 48V Hybrid Electric...
Article Real-Time Reinforcement Learning Optimized Energy Management...
Load change is considered an external stressor that adversely impacts the failure rate (lambda) of the battery and, thus, impacts its mean time between failure (MTBF).
There are theoretical models that can predict battery's MTBF but the more accurate approach is to experimentally subject the battery to cyclic load changes using the so-called highly accelerated life testing (HALT).