The methods of recurrence plots (RPs) and recurrence quantification analysis (RQA) have been used to investigate the tribosystem. The morphology of RPs and RQA measures are strongly dependent on the embedding parameters of the recursive matrix and the segment sizes of the time-series. To improve the calculation accuracy of recursive characteristics analysis, the influences of the embedding parameters and segment sizes on the morphology of RPs and RQA measures have been studied in this letter. Three kinds of theoretical chaotic time-series and measured coefficient of friction (COF) signals during the running-in process were chosen as research objects, and the morphology of RPs and RQA measures were obtained using CRP toolbox afterward. The results indicate that no embedding was actually needed if the data sets are to be qualitatively analyzed using RPs and RQA. Additionally, the morphology of RPs and RQA measures are sensitive to the segment sizes for theoretical chaotic time-series, while the RQA measures of COF signal in the steady-state period are rather stable due to its self-similarity. Finally, according to the guidelines of the parameter settings, the dynamical evolution of measured COF signals during the running-in process have been investigated. It is indicated that recursive characteristics of COF signals could reveal the tribological behaviors’ evolution and conduct the running-in status identification. The results in this paper are significant for improving the calculation accuracy and saving computational time when using the method of recursive characteristics analysis on the tribological behaviors.

中文翻译：

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递归特性分析中嵌入参数和分段大小对摩擦系数的影响

递归图 (RPs) 和递归量化分析 (RQA) 方法已被用于研究摩擦系统。RPs 和 RQA 度量的形态很大程度上取决于递归矩阵的嵌入参数和时间序列的段大小。为了提高递归特征分析的计算精度，本文研究了嵌入参数和段大小对RPs形态和RQA度量的影响。以磨合过程中的三种理论混沌时间序列和实测摩擦系数（COF）信号为研究对象，随后使用CRP工具箱获得RPs的形态和RQA措施。结果表明，如果要使用 RP 和 RQA 对数据集进行定性分析，则实际上不需要嵌入。此外，RPs 和 RQA 测量的形态对理论混沌时间序列的段大小敏感，而稳态期间 COF 信号的 RQA 测量由于其自相似性而相当稳定。最后，根据参数设置的指导方针，研究了磨合过程中测量的COF信号的动态演变。结果表明，COF信号的递归特性可以揭示摩擦学行为的演变，并进行磨合状态识别。