Non-destructive diagnostics of electric parking brake modules using recurrence analysis of piezoelectric sensor data

Abstract This paper presents a non-invasive diagnostic approach for Electric Parking Brake (EPB) modules based on recurrence quantification analysis (RQA) of piezoelectric vibration data. Vibration signals were collected from sensors mounted on the motor, planetary gearbox, and pinion under five predefined fault conditions: missing gear in the lower row of the planetary gearbox, missing gear in the upper row, tooth damage in the planetary gear, partially cut timing belt, and incorrect gear installation. Each failure mode was tested repeatedly to obtain statistically reliable datasets for non-linear time-series and recurrence-based analysis. The following RQA quantificators were computed: Determinism (DET), Laminarity (LAM), maximal diagonal line length ( $$L_{\max }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>L</mml:mi> <mml:mo>max</mml:mo> </mml:msub> </mml:math> ), and mean diagonal line length ( L ) were calculated to characterize the underlying dynamic behavior. Additional recurrence quantificators describing laminar states—Trapping Time (TT) and maximal vertical line length ( $$V_{\max }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>V</mml:mi> <mml:mo>max</mml:mo> </mml:msub> </mml:math> ) were used to capture transient stability and synchronization effects. The results show that these RQA quantificators are highly sensitive to mechanical faults, especially within the gearbox, enabling effective fault localization and differentiation between failure types. The missing-gear condition resulted in increased values of DET, LAM, and $$L_{\max }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>L</mml:mi> <mml:mo>max</mml:mo> </mml:msub> </mml:math> , reflecting more regular and structured recurrence patterns, while incorrect pinion installation produced more irregular and weakly correlated responses. Statistical analyses confirmed that the observed differences between fault conditions were significant, not only within experimental groups, but also between individual RQA quantificators, highlighting their diagnostic discriminative capability. The proposed method allows efficient fault detection without disassembling the EPB unit, thus reducing remanufacturing costs and downtime. Overall, the study demonstrates that recurrence-based diagnostics provide a robust and interpretable framework for real-time condition monitoring and fault prediction.