• Journal of Electronic Science and Technology
  • Vol. 22, Issue 4, 100285 (2024)
Yi-Feng Li1, Zhi-Ang Hu1, Jia-Wei Gao1, Yi-Sheng Zhang1..., Peng-Fei Li2 and Hai-Zhou Du2,*|Show fewer author(s)
Author Affiliations
  • 1Shanghai Electric Power Energy Technology Co., Ltd., Shanghai, 200233, China
  • 2School of Computer Science and Technology, Shanghai University of Electric Power, Shanghai, 201306, China
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    DOI: 10.1016/j.jnlest.2024.100285 Cite this Article
    Yi-Feng Li, Zhi-Ang Hu, Jia-Wei Gao, Yi-Sheng Zhang, Peng-Fei Li, Hai-Zhou Du. Efficient anomaly detection method for offshore wind turbines[J]. Journal of Electronic Science and Technology, 2024, 22(4): 100285 Copy Citation Text show less

    Abstract

    Time-series anomaly detection plays a crucial role in the operation of offshore wind turbines. Various wind turbine monitoring systems rely on time-series data to monitor and identify anomalies in real-time, as well as to initiate early warning processes. However, for offshore wind turbines with a high data density, conventional methods have high computational overhead in detecting anomalies while failing to accurately detect anomalies due to variations in data scales. To address this challenge, we propose an efficient anomaly detection method with contrastive learning, called Hawkeye. Hawkeye is based on residual clustering, an unsupervised anomaly detection method for multivariate time-series data. To ensure accurate anomaly detection, a trend-capturing prediction module is also combined with an automatic labeling module. As a result, the most common information can be learned from multivariate time-series data to reconstruct data trends. By evaluating Hawkeye on public datasets and real-world offshore wind turbine operational datasets, the results show that Hawkeye’s F1-score improves by an average of 14% compared with Isolation Forest, and its size shrinks by up to 11.5 times on the largest dataset compared with other methods. The proposed Hawkeye is potential to real-time monitoring and early warning systems for wind turbines, accelerating the development of intelligent operation and maintenance.
    $ \delta = \text{Hawkeye}({{\bf{x}}}_{1:T}) $(1)

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    $ \delta = \left\{ {0, normal data1, anomalous data} \right. $(2)

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    $ L({{\mathbf{x}}_{i{\mathrm{,}}j}}) = \sum\limits_{k = 0}^N {{y_{i + k{\mathrm{,}}j}}} \prod\limits_{m = 0{\mathrm{,}}m \ne k}^N {\frac{{{{\mathbf{x}}_{i{\mathrm{,}}j}} - {{\mathbf{x}}_{i + m{\mathrm{,}}j}}}}{{{{\mathbf{x}}_{i + k{\mathrm{,}}j}} - {{\mathbf{x}}_{i + m{\mathrm{,}}j}}}}} $(3)

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    $ Z{\text{-score}} = \frac{{x - \mu }}{\sigma } $(4)

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    $ {{\mathbf{x}}_{1:T}} = \left\{ {{\mathbf{x}}_{i{\mathrm{,}}d}^{(e)}|1 \leq i \leq {T \mathord{\left/ {\vphantom {T {{\text{LE}}{{\text{N}}_{{\text{eps}}}}}}} \right. } {{\text{LE}}{{\text{N}}_{{\text{eps}}}}}}{\mathrm{,}}{\text{ }}1 \leq d \leq D} \right\} $(5)

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    $ {\mathbf{x}}_{i{\mathrm{,}}d}^{(e)} = \left\{ {{{\mathbf{x}}_{t{\mathrm{,}}d}}|(i - 1) \times {\text{LE}}{{\text{N}}_{{\text{eps}}}} < t \leq i \times {\text{LE}}{{\text{N}}_{{\text{eps}}}}} \right\} $(6)

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    $ {{\mathbf{h}}_{i{\mathrm{,}}d}} = {\mathbf{{\rm E}}}_{i{\mathrm{,}}d}^{(e)} + {\mathbf{E}}_{i{\mathrm{,}}d}^{({\text{pos}})}. $(7)

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    $ \widehat {\mathbf{Z}}_{:{\mathrm{,}}d}^t = {\text{LayerNorm}}\left( {{\mathbf{Z}}_{:{\mathrm{,}}d}^t + {\text{MS}}{{\text{A}}^t}\left( {{{\mathbf{Z}}_{:{\mathrm{,}}d}}{\mathrm{,}}{\text{ }}{{\mathbf{Z}}_{:{\mathrm{,}}d}}{\mathrm{,}}{\text{ }}{{\mathbf{Z}}_{:{\mathrm{,}}d}}} \right)} \right) $(8)

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    $ {{\mathbf{Z}}^t} = {\text{LayerNorm}}\left( {{{\widehat {\mathbf{Z}}}^t} + {\text{MLP}}\left( {{{\widehat {\mathbf{Z}}}^t}} \right)} \right) $(9)

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    $ \left\{ {l=0:Z^enc,l=Hl>1:Z^i,denc,l=M[Z2i1,denc,l1Z2i,denc,l1]} \right. $(10)

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    $ {{\mathbf{Z}}^{{\text{enc}}{\mathrm{,}}l}} = {\text{TSA}}\left( {{{\widehat {\mathbf{Z}}}^{{\text{enc}}{\mathrm{,}}l}}} \right) $(11)

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    $ \left\{ {l=0:Z~dec,l=TSA(E(dec))l>0:Z~dec,l=TSA(Zdec,l1)} \right. $(12)

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    $ \overline {\mathbf{Z}} _{:{\mathrm{,}}d}^{{\text{dec}}{\mathrm{,}}l} = {\text{MSA}}\left( {\widetilde {\mathbf{Z}}_{:{\mathrm{,}}d}^{{\text{dec}}{\mathrm{,}}l}{\mathrm{,}}{\text{ }}{\mathbf{Z}}_{:{\mathrm{,}}d}^{{\text{enc}}{\mathrm{,}}l}{\mathrm{,}}{\text{ }}{\mathbf{Z}}_{:{\mathrm{,}}d}^{{\text{enc}}{\mathrm{,}}l}} \right) $(13)

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    $ {\widehat {\mathbf{Z}}^{{\text{dec}}{\mathrm{,}}l}} = {\text{LayerNorm}}\left( {{{\widetilde {\mathbf{Z}}}^{{\text{dec}}{\mathrm{,}}l}} + {{\overline {\mathbf{Z}} }^{{\text{dec}}{\mathrm{,}}l}}} \right) $(14)

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    $ {{\mathbf{Z}}^{{\text{dec}}{\mathrm{,}}l}} = {\text{LayerNorm}}\left( {{{\widehat {\mathbf{Z}}}^{{\text{dec}}{\mathrm{,}}l}} + {\text{MLP}}\left( {{{\widehat {\mathbf{Z}}}^{{\text{dec}}{\mathrm{,}}l}}} \right)} \right) $(15)

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    $ {U^*} = {\mathrm{arg}}\, {{\mathrm{min}} _{{\mathbf{U}} \in {{\{ 0{\mathrm{,}}1\} }^{k \times n}}}}{{\mathrm{max}} _{{c_k} \in \chi }}\sum\limits_{k = 1}^C {\sum\limits_{i = 1}^N {{U_{k{\mathrm{,}}i}}} } ||{c_k} - {r_i}||_d^2 $(16)

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    $ \mathrm{min}\, J = \sum\limits_{t = 1}^N {\sum\limits_{k = 1}^K {{I_{t{\mathrm{,}}k}}} } ||{r_t} - {\mu _k}|{|^2} $(17)

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    $ {\hat I_{t{\mathrm{,}}k}} = \left\{ {1,k=argmink||rtμk||20,otherwise} \right. $()

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    $ ||{r_t} - {\mu _k}|{|^2} \geq {{\mathrm{min}} _{k'}}||{r_t} - {\mu _{k'}}|{|^2} $()

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    $ \sum\limits_{k = 1}^K {\left( {{I_{t{\mathrm{,}}k}}||{r_t} - {\mu _k}|{|^2}} \right)} {\text{ }} \geq \sum\limits_{k = 1}^K {\left( {{I_{t{\mathrm{,}}k}}{{{\mathrm{min}} }_{k'}}||{r_t} - {\mu _{k'}}|{|^2}} \right)} $()

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    $ {\mathrm{min} _{k'}}||{r_t} - {\mu _{k'}}|{|^2} = \sum\limits_{k = 1}^K {\left( {{{\hat I}_{t{\mathrm{,}}k}}||{r_t} - {\mu _k}|{|^2}} \right)} $()

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    $ \sum\limits_{k = 1}^K {\left( {{I_{t{\mathrm{,}}k}}||{r_t} - {\mu _k}|{|^2}} \right)} \geq {\mathrm{min} _{k'}}||{r_t} - {\mu _{k'}}|{|^2} $()

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    $ {\nabla _{{\mu _k}}}J = \sum\limits_{t = 1}^N {{I_{t{\mathrm{,}}k}}} {\nabla _{{\mu _k}}}{({r_t} - {\mu _k})^T}({r_t} - {\mu _k}) $()

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    $ {\nabla _{{\mu _k}}}J = 2\sum\limits_{t = 1}^N {{I_{t{\mathrm{,}}k}}} ({\mu _k} - {r_t}) = 0 $()

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    $ {\hat \mu _k} = {{\displaystyle\sum\limits_{t = 1}^N {({I_{t{\mathrm{,}}k}}{r_t})} }}\Big/{{\displaystyle\sum\limits_{t = 1}^N {{r_{t{\mathrm{,}}k}}} }}. $()

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    $ {\nabla _{{\mu _k}}}J = 2\sum\limits_{t = 1}^N {{I_{t{\mathrm{,}}k}}} ({\mu _k} - {r_t}) = 0 $()

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    $ {\nabla _{{\mu _k}}}({\nabla _{{\mu _k}}}J) = \left( {2\sum\limits_{t = 1}^N {{I_{t{\mathrm{,}}k}}} } \right)I \succ 0. $()

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    $ P = \frac{{\displaystyle\sum\limits_{i = 1}^N {{w_i}} \times {\text{Precisio}}{{\text{n}}_i}}}{{\displaystyle\sum\limits_{i = 1}^N {{w_i}} }} $(18)

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    $ R = \frac{{\displaystyle\sum\limits_{i = 1}^N {{w_i}} \times {\text{Recal}}{{\text{l}}_i}}}{{\displaystyle\sum\limits_{i = 1}^N {{w_i}} }} $(19)

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    $ {F_{\text{1}}}{{ = }}\frac{{\displaystyle\sum\limits_{i{{ = 1}}}^N {{w_i}} \times {F_{\text{1}}}{\text{-scor}}{{\text{e}}_i}}}{{\displaystyle\sum\limits_{i{{ = 1}}}^N {{w_i}} }} $(20)

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    $ {\text{Precisio}}{{\text{n}}_i} = \frac{{{\text{T}}{{\text{P}}_i}}}{{{\text{T}}{{\text{P}}_i} + {\text{F}}{{\text{P}}_i}}} $(21)

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    $ {\text{Recal}}{{\text{l}}_i} = \frac{{{\text{T}}{{\text{P}}_i}}}{{{\text{T}}{{\text{P}}_i} + {\text{F}}{{\text{N}}_i}}} $(22)

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    $ {F_{\text{1}}}{\text{-scor}}{{\text{e}}_i}{\text{ = }}\frac{{{\text{2}} \times {\text{Precisio}}{{\text{n}}_i} \times {\text{Recal}}{{\text{l}}_i}}}{{{\text{Precisio}}{{\text{n}}_i}{\text{ + Recal}}{{\text{l}}_i}}} $(23)

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    Yi-Feng Li, Zhi-Ang Hu, Jia-Wei Gao, Yi-Sheng Zhang, Peng-Fei Li, Hai-Zhou Du. Efficient anomaly detection method for offshore wind turbines[J]. Journal of Electronic Science and Technology, 2024, 22(4): 100285
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