The Preisach model is the most widely used hysteresis model due to its ability to capture a wide range of hysteresis shapes and its relatively simple mathematical structure.
Overview
Classical Preisach model
Advantages:
- Versatility: It can model a variety of hysteresis shapes, including those with complex minor loops and memory effects.
- Simplicity: The underlying concept of the model is relatively straightforward, involving an assembly of simple relay-type elements.
- Mathematical tractability: The model often allows for analytical solutions or efficient numerical computations.
Disadvantages:
- Parameter identification: Determining the parameters of the Preisach model, particularly the weight function, can be challenging and often requires sophisticated algorithms.
- Rate independence: The classical Preisach model is inherently rate-independent, meaning it doesn’t account for the speed of the input signal. This limitation can be addressed by modifications to the model, but it adds complexity.
- Physical interpretation: The physical interpretation of the model parameters may not always be straightforward, making it difficult to relate the model to the underlying physical mechanisms of the system.
Differentiable Preisach model
A differentiable preisach model proposed by @rousselDifferentiablePreisachModeling2022 allows simpler parameter identification by making the hysterons differentiable using sigmoid gates, and assigning a weight to each hysteron, where each hysteron is generated as a point in a triangular mesh.
Through fitting the differentiable preisach model to measured SPS MBI data (with calibration function removed), mapping (instead of ), we achieve the following: