Alkaline Water Electrolysis (AWE) is one of the simplest green hydrogen
production method using renewable energy.
AWE system typically yields process variables that are serially correlated
and contaminated by measurement uncertainty.
A novel robust dynamic variational Bayesian dictionary learning (RDVDL)
monitoring approach is proposed to improve the reliability and safety of AWE
operation.
RDVDL employs a sparse Bayesian dictionary learning to preserve the dynamic
mechanism information of AWE process which allows the easy interpretation of
fault detection results.
To improve the robustness to measurement uncertainty, a low-rank vector
autoregressive (VAR) method is derived to reliably extract the serial
correlation from process variables.
The effectiveness of the proposed approach is demonstrated with an industrial
hydrogen production process, and RDVDL can efficiently detect and diagnose
critical AWE faults.

提出一种新的稳健动态变分贝叶斯字典学习（RDVDL）监测方法，以提高碱性水电解（AWE）操作的可靠性和安全性。RDVDL 采用稀疏贝叶斯字典学习来保留 AWE 过程的动态机制信息，从而容易解释故障检测结果。为了提高对测量不确定性的鲁棒性，提出了一种低秩矢量自回归（VAR）方法，可可靠地提取出过程变量的串行相关性。该方法在工业氢气生产过程中得到了有效验证，RDVDL 能够高效地检测和诊断关键的 AWE 故障。

工业碱性水电解槽动态故障检测与诊断的变分贝叶斯字典学习方法

Dynamic fault detection and diagnosis of industrial alkaline water  electrolyzer process with variational Bayesian dictionary learning

In the context of industrially mass-manufactured products, quality management
is based on physically inspecting a small sample from a large batch and
reasoning about the batch's quality conformance. When complementing physical
inspections with predictions from machine learning models, it is crucial that
the uncertainty of the prediction is known. Otherwise, the application of
established quality management concepts is not legitimate. Deterministic
(machine learning) models lack quantification of their predictive uncertainty
and are therefore unsuitable. Probabilistic (machine learning) models provide a
predictive uncertainty along with the prediction. However, a concise
relationship is missing between the measurement uncertainty of physical
inspections and the predictive uncertainty of probabilistic models in their
application in quality management. Here, we show how the predictive uncertainty
of probabilistic (machine learning) models is related to the measurement
uncertainty of physical inspections. This enables the use of probabilistic
models for virtual inspections and integrates them into existing quality
management concepts. Thus, we can provide a virtual measurement for any quality
characteristic based on the process data and achieve a 100 percent inspection
rate. In the field of Predictive Quality, the virtual measurement is of great
interest. Based on our results, physical inspections with a low sampling rate
can be accompanied by virtual measurements that allow an inspection rate of 100
percent. We add substantial value, especially to complex process chains, as
faulty products/parts are identified promptly and upcoming process steps can be
aborted.

通过将机器学习模型的预测不确定性与实际物理检测的测量不确定性联系起来，可以在质量管理中使用概率模型进行虚拟检测，并将其融入现有质量管理概念，从而实现对过程数据的全面测量，提高检测率并及时识别缺陷产品 / 零件。

测量不确定性：关联物理和虚拟测量的不确定性

Measurement Uncertainty: Relating the uncertainties of physical and  virtual measurements

We derive a Bayesian framework for incorporating selection effects into
population analyses. We allow for both measurement uncertainty in individual
measurements and, crucially, for selection biases on the population of
measurements, and show how to extract the parameters of the underlying
distribution based on a set of observations sampled from this distribution. We
illustrate the performance of this framework with an example from
gravitational-wave astrophysics, demonstrating that the mass ratio distribution
of merging compact-object binaries can be extracted from Malmquist-biased
observations with substantial measurement uncertainty.

提出了一种贝叶斯框架，用于将选择效应纳入人口分析中，并展示了如何从一个样本中提取基础分布的参数。演示了该框架的性能，从引力波天体物理学的例子中证明合并紧凑物体二元的质量比分布可以从具有实质性测量不确定性的 Malmquist 偏差观测中提取。