Abstract Train wheelset is an important part of the train. After long-time and high load working, fatigue damage will appear. Then the micro-cracks will form and expand into macro cracks, which may cause a serious accident. Therefore, it is necessary to study the fatigue damage detection methods for train wheelset. Fatigue damage will cause nonlinear effects. The Nonlinear Output Frequency Response Functions (NOFRFs) is an effective tool to characterize the nonlinearity of the system. In this paper, based on the concept of Kull Back-Leibler (KL) divergence and NOFRFs, a detection method denoted as NOFRFs-KL (NKL) is proposed to study the feasibility of comprehensively evaluate the fatigue damage of wheelset. The train wheelset is considered as a single input multiple output (SIMO) nonlinear system while hammering on one point in the hammering test. And the estimated NOFRFs of multiple positions in the SIMO system are used to evaluate the fatigue damage at each output position. To verify the effectiveness of the NKL, some hammering tests are carried out. The NOFRFs of the wheelsets with micro-cracks, repaired wheelsets are calculated. The NOFRFs of the wheelsets with different served time are calculated. And then the corresponding NKL values are obtained. The results show that the fatigue damage in the wheelsets can be identified by the NKL index, and the NKL index can be proportional to the service time of the wheelset.

中文翻译：

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SIMO中NOFRFs-KL散度检测方法轮对疲劳损伤可行性研究

摘要 列车轮对是列车的重要组成部分。长时间高负荷工作后，会出现疲劳损伤。然后微裂纹会形成并扩展为宏观裂纹，这可能会导致严重的事故。因此，有必要研究列车轮对疲劳损伤检测方法。疲劳损伤会引起非线性效应。非线性输出频率响应函数 (NOFRF) 是表征系统非线性的有效工具。本文基于Kull Back-Leibler（KL）散度和NOFRFs的概念，提出了一种称为NOFRFs-KL（NKL）的检测方法，以研究综合评估轮对疲劳损伤的可行性。在锤击试验中锤击某一点时，列车轮对被视为单输入多输出 (SIMO) 非线性系统。并利用 SIMO 系统中多个位置的估计 NOFRFs 来评估每个输出位置的疲劳损伤。为了验证 NKL 的有效性，进行了一些锤击测试。计算有微裂纹的轮对、修复轮对的 NOFRF。计算不同服务时间轮对的NOFRFs。然后得到相应的NKL值。结果表明，通过NKL指数可以识别轮对的疲劳损伤，并且NKL指数可以与轮对的使用时间成正比。计算修复的轮对。计算不同服务时间轮对的NOFRFs。然后得到相应的NKL值。结果表明，通过NKL指数可以识别轮对的疲劳损伤，并且NKL指数可以与轮对的使用时间成正比。计算修复的轮对。计算不同服务时间轮对的NOFRFs。然后得到相应的NKL值。结果表明，通过NKL指数可以识别轮对的疲劳损伤，并且NKL指数可以与轮对的使用时间成正比。