Data-driven Power Loss Identification through Physics-Based Thermal Model Backpropagation

The paper Data-driven Power Loss Identification through Physics-Based Thermal Model Backpropagation presents a novel hybrid framework that combines physics-based thermal modeling with data-driven techniques to identify and correct power losses accurately using only temperature measurements. This approach is designed for digital twins in power electronics, where accurate power losses whose direct measurements are often impractical or impossible in real-world applications are required for effective thermal management.

The proposed methodology utilizes a cascaded architecture where a neural network learns to correct the outputs of a nominal power loss model by backpropagating through a reduced-order thermal model. The system consists of two primary components: a Power Loss Model (PLM) and a Thermal Model (TM). The TM is a parameterized linear state space representation derived from a Reduced Order Model (ROM) through a model reduction process from high-fidelity Finite Element Method (FEM) simulation. The PLM is a parameterized function that maps inputs to power losses, but it often suffers from uncertainties due to manufacturing tolerance, device materials properties and geometry.

To correct these errors, the authors propose a "data-driven correction approach that acts directly on the Power Loss (PL) outputs by adopting a function f omega(times), which in our analysis is a neural network parameterized by omega in R, acting as a correction function. The training process exploits the fact that all the operations are differentiable, allowing the use of backpropagation through the physics-based thermal model guiding the network updates to get physical meaning." The paper evaluates two neural architectures:

1. Feedforward Neural Network (FNN): Implemented as a MultiLayer Perceptron (MLP), this architecture uses TM normalization to mitigate vanishing gradient issues and correction instabilities. By setting the activation function to hyperbolic tangent, i.e., tanh, the authors ensure that loss corrections, and consequently the temperature estimations, are always bounded. Furthermore, they introduce a Bootstrap Implementation to address the fact that the data used to train the network also change as the neural network's parameters update. This strategy involves periodically simulating the hybrid model to collect the new generated trajectories for training.

2. Recurrent Neural Network (RNN): Specifically an Elman’s Network derivation, which introduces an additional internal state that allows modeling dynamics, a useful property for time series prediction.

The training is governed by a physics-informed loss function designed to preserve stability and ensure physical consistency. The loss function is defined as L omega = MSE(y, omega) + alpha (u omega) + beta epsilon u, omega 2. This includes a penalty [that] penalizes the losses u omega when negative and a regularization term that constrains the correction to be "within a factor zeta > 0, representing the confidence of our nominal model."

Experimental results demonstrate that the hybrid model reduces both temperature estimation errors (from 7.2±6.8°C to 0.3±0.3°C) and power loss prediction errors (from 5.4±6.6W to 0.2±0.3W) compared to traditional physics-based approaches. The FNN architecture with bootstrap implementation achieves significantly better performance compared to RNN configurations in both scenarios (Accurate TM and Noisy TM). Sensitivity analysis confirmed that the thermal model effectively provides physical guidance, noting that when the gradient magnitude is smaller, the reconstruction loss is higher. Finally, in a Real Scenario involving an inlet charger for electrical vehicles, the proposed scheme achieved high accuracy and successfully correct[ed] the biases of the nominal power loss.

1. Bayesian Uncertainty Quantification Integration

• Improvement: Replace the deterministic neural network f omega(times) with a Bayesian Neural Network (BNN) or a Deep Ensemble approach to estimate epistemic and aleatoric uncertainty.

• Improved Capability: The system can provide real-time confidence intervals for every power loss and temperature prediction. This allows the digital twin to distinguish between low error and high uncertainty, enabling the power electronics controller to trigger safe mode or maintenance required protocols when the model encounters operating conditions outside its training distribution.

2. Non-linear Differentiable Physics via Neural ODEs

• Improvement: Replace the parameterized linear state-space Thermal Model (TM) with a Neural Ordinary Differential Equation (Neural ODE) framework that incorporates non-linear thermal properties.

• Improved Capability: The system can accurately model temperature-dependent thermal conductivity and non-linear heat dissipation (e.g., radiation or variable fan speeds), allowing for high-fidelity thermal management even during extreme temperature excursions where linear approximations fail.

3. Attention-Based Temporal Modeling

• Improvement: Replace the Elman RNN architecture with a Temporal Fusion Transformer (TFT) or a Gated Recurrent Unit (GRU) with multi-head attention mechanisms.

• Improved Capability: The system can better capture long-range temporal dependencies and transient thermal memory effects during complex, non-periodic power cycling, significantly improving prediction accuracy during rapid load transitions in electric vehicle chargers.

4. Online Continual Learning for Component Aging

• Improvement: Implement an Online Continual Learning framework using Experience Replay to update the correction function f omega(times) incrementally.

• Improved Capability: The system can autonomously adapt to the physical degradation of components (such as the drying of thermal interface materials or aging of capacitors) in real-time, ensuring the digital twin remains accurate over the entire multi-year lifecycle of the power electronic device without requiring periodic full-scale simulations.

5. Multi-Modal Physics-Informed Loss Functions

• Improvement: Expand the loss function L omega to include a Physics-Informed Neural Network (PINN) component that penalizes violations of the underlying Heat Diffusion Partial Differential Equations (PDEs), rather than just backpropagating through a ROM.

• Improved Capability: The system can maintain strict physical consistency even when sensor data is noisy or missing, preventing the correction from proposing power loss values that are mathematically possible but physically impossible according to the laws of thermodynamics.

6. Multi-Sensor Input Fusion

• Improvement: Transition the Power Loss Model (PLM) from a simple mapping to a multi-modal architecture that ingests synchronized streams of voltage, current, ambient temperature, and cooling flow rates.

• Improved Capability: The system can decouple the effects of varying electrical loads from environmental fluctuations (e.g., a hot day vs. a high-load event), allowing for much more precise identification of internal power losses versus external environmental influence.