This paper presents a new observer-based approach to detect and isolate
faulty sensors in industrial systems. Two types of sensor faults are
considered: complete failure and sensor deterioration. The proposed method is
applicable to general autonomous nonlinear systems without making any
assumptions about its triangular and/or normal form, which is usually
considered in the observer design literature. The key aspect of our approach is
a learning-based design of the Luenberger observer, which involves using a
neural network to approximate the injective map that transforms the nonlinear
system into a stable linear system with output injection. This learning-based
Luenberger observer accurately estimates the system's state, allowing for the
detection of sensor faults through residual generation. The residual is
computed as the norm of the difference between the system's measured output and
the observer's predicted output vectors. Fault isolation is achieved by
comparing each sensor's measurement with its corresponding predicted value. We
demonstrate the effectiveness of our approach in capturing and isolating sensor
faults while remaining robust in the presence of measurement noise and system
uncertainty. We validate our method through numerical simulations of sensor
faults in a network of Kuramoto oscillators.

本文提出了一种新的基于观察者的方法来检测和隔离工业系统中的故障传感器，其中考虑了两种类型的传感器故障，即完全故障和传感器劣化。这种基于学习的 Luenberger 观察器可以准确估计系统状态，从而通过残差产生检测传感器故障，并且能够在测量噪声和系统不确定性存在的情况下保持稳健，在 Kuramoto 振荡器网络中进行数值模拟以验证该方法的有效性。

基于神经网络观测器的自主非线性系统传感器故障检测与隔离

Sensor Fault Detection and Isolation in Autonomous Nonlinear Systems  Using Neural Network-Based Observers

We use topological data analysis to study "functional networks" that we
construct from time-series data from both experimental and synthetic sources.
We use persistent homology with a weight rank clique filtration to gain
insights into these functional networks, and we use persistence landscapes to
interpret our results. Our first example uses time-series output from networks
of coupled Kuramoto oscillators. Our second example consists of biological data
in the form of functional magnetic resonance imaging (fMRI) data that was
acquired from human subjects during a simple motor-learning task in which
subjects were monitored on three days in a five-day period. With these
examples, we demonstrate that (1) using persistent homology to study functional
networks provides fascinating insights into their properties and (2) the
position of the features in a filtration can sometimes play a more vital role
than persistence in the interpretation of topological features, even though
conventionally the latter is used to distinguish between signal and noise. We
find that persistent homology can detect differences in synchronization
patterns in our data sets over time, giving insight both on changes in
community structure in the networks and on increased synchronization between
brain regions that form loops in a functional network during motor learning.
For the motor-learning data, persistence landscapes also reveal that on average
the majority of changes in the network loops take place on the second of the
three days of the learning process.

使用拓扑数据分析方法研究实验和人工来源的时间序列数据所构造的 “功能网络”。使用持久性同调与加权等阶团过滤来深入挖掘功能网络，使用持续地形图来解释结果，表明持续同调可以检测数据集中随时间出现的同步模式的差异，从而揭示网络社群结构的变化和学习过程中形成回路的脑区之间的同步增强。