Testing Topological Data Analysis for Condition Monitoring of Wind Turbines

TL;DR

This work explores applying topological data analysis (TDA) to condition-based monitoring of wind-turbine gearboxes by transforming high-frequency vibration time series into time-delay embedded point clouds and extracting topology-based indicators from persistence diagrams. It combines spectral analysis with TDA, using indicators such as the maximum persistence $\mathcal{P}^{H_k}_{\infty}$, normalized persistence entropy $\overline{\textrm{E}}_{H_k}(D)$, Betti curves $\beta_k$, and $f$-indicators from persistence diagrams $D$ to detect faults in bearing and gear-tooth components. The results show that bearing faults can cause a shift away from toroidal topology and provoke distinct changes in topological indicators prior to failure, while gear-tooth faults produce pre-failure topology changes coupled with spectral cues, demonstrating the complementary value of TDA for CBM. Overall, the study provides evidence that topology-based features can enhance early fault detection and diagnosis in wind turbine gearboxes, with potential for real-time monitoring and maintenance planning.

Abstract

We present an investigation of how topological data analysis (TDA) can be applied to condition-based monitoring (CBM) of wind turbines for energy generation. TDA is a branch of data analysis focusing on extracting meaningful information from complex datasets by analyzing their structure in state space and computing their underlying topological features. By representing data in a high-dimensional state space, TDA enables the identification of patterns, anomalies, and trends in the data that may not be apparent through traditional signal processing methods. For this study, wind turbine data was acquired from a wind park in Norway via standard vibration sensors at different locations of the turbine's gearbox. Both the vibration acceleration data and its frequency spectra were recorded at infrequent intervals for a few seconds at high frequency and failure events were labelled as either gear-tooth or ball-bearing failures. The data processing and analysis are based on a pipeline where the time series data is first split into intervals and then transformed into multi-dimensional point clouds via a time-delay embedding. The shape of the point cloud is analyzed with topological methods such as persistent homology to generate topology-based key health indicators based on Betti numbers, information entropy and signal persistence. Such indicators are tested for CBM and diagnosis (fault detection) to identify faults in wind turbines and classify them accordingly. Topological indicators are shown to be an interesting alternative for failure identification and diagnosis of operational failures in wind turbines.

Figures (12)

• Figure 1: Overview of how the gearbox vibration data are processed by means of topological data analysis.
• Figure 2: Left to right: Raw time-series signal, embedded point cloud and persistence diagram for GbxHssFr sensor at normal operation state. Note the toroidal point cloud, resulting from the embedding of the periodic time series. The loop structure is revealed in the persistence diagram as a point (yellow) far from the diagonal, where points created by signal noise tend to accumulate.
• Figure 3: Fourier transform (normalised to counts) of the signal recorded on 2023-10-28 for GnNDe-BBF and GbxHssFr-BBF. The vertical lines indicate the frequency intervals for which the most dominating peaks are investigated for GbxHssFr.
• Figure 4: Peak height (left axis, circles) and width (right axis, crosses) for three frequency signatures (most dominant peak in the frequency ranges [1000, 1800], [1800, 2300], [2300, 3000] Hz) for GbxHssFr in the bearing failure case.
• Figure 5: Topological indicators computed for the signal GbxHssFr in the bearing failure case. Highlighted the most significant anomaly, dated 2023-10-08.