Machine learning plays an important role in the operation of current wind
energy production systems. One central application is predictive maintenance to
increase efficiency and lower electricity costs by reducing downtimes.
Integrating physics-based knowledge in neural networks to enforce their
physical plausibilty is a promising method to improve current approaches, but
incomplete system information often impedes their application in real world
scenarios. We describe a simple and efficient way for physics-constrained deep
learning-based predictive maintenance for wind turbine gearbox bearings with
partial system knowledge. The approach is based on temperature nowcasting
constrained by physics, where unknown system coefficients are treated as
learnable neural network parameters. Results show improved generalization
performance to unseen environments compared to a baseline neural network, which
is especially important in low data scenarios often encountered in real-world
applications.

基于物理约束的深度学习技术在风能预测性维护中发挥重要作用，特别适用于部分系统信息不完整的实际应用场景。

基于物理约束的循环神经网络的通用化温度预测模型 在风力涡轮机组件预测性维护中的应用

Generalizable Temperature Nowcasting with Physics-Constrained RNNs for  Predictive Maintenance of Wind Turbine Components

Effective inclusion of physics-based knowledge into deep neural network
models of dynamical systems can greatly improve data efficiency and
generalization. Such a-priori knowledge might arise from physical principles
(e.g., conservation laws) or from the system's design (e.g., the Jacobian
matrix of a robot), even if large portions of the system dynamics remain
unknown. We develop a framework to learn dynamics models from trajectory data
while incorporating a-priori system knowledge as inductive bias. More
specifically, the proposed framework uses physics-based side information to
inform the structure of the neural network itself, and to place constraints on
the values of the outputs and the internal states of the model. It represents
the system's vector field as a composition of known and unknown functions, the
latter of which are parametrized by neural networks. The physics-informed
constraints are enforced via the augmented Lagrangian method during the model's
training. We experimentally demonstrate the benefits of the proposed approach
on a variety of dynamical systems -- including a benchmark suite of robotics
environments featuring large state spaces, non-linear dynamics, external
forces, contact forces, and control inputs. By exploiting a-priori system
knowledge during training, the proposed approach learns to predict the system
dynamics two orders of magnitude more accurately than a baseline approach that
does not include prior knowledge, given the same training dataset.

利用物理学基础知识作为先验知识，通过将物理学基础知识注入到神经网络结构中，从轨迹数据中学习动力学模型，并在模型的训练过程中通过增广拉格朗日法强制实施物理学知识约束，实验证明该做法比不包括先验知识的基线方法在相同的训练数据集上能够将系统动力学预测准确率提升两个数量级。