现有的基于混沌振子检测轴承故障的方法的关键步骤是混沌振子相态转变判别,目前大多采用李雅普诺夫指数等特征值进行判断，针对其计算过程复杂，耗费时间长的缺点，基于图像识别技术，提出了一种以极半径不变矩参数作为相态转变的识别方法。通过构造Duffing混沌振子，分析了其相态转变与周期策动力的变化关系，证明其用于轴承早期故障识别的可行性；给出了极半径不变矩的定义，并证明在混沌振子相图由混沌运动态向大尺度周期态转变的过程中，随着周期摄动力不断增加，极半径不变矩表现出单调递增的特性；与HU氏不变矩及二维近似熵判别方法进行对比，讨论了极半径不变矩的抗噪声干扰能力；最终，将该方法用于实际搭建的钻机动力头轴承早期故障诊断的试验中。试验结果表明：极半径不变矩可以识别混沌振子相态过程转变，最低检测信噪比达到-36.99 dB，且识别准确率也较另外两种方法提高了4%~7%。证明该方法可以用于轴承早期故障识别，具有识别准确率高，抗噪声干扰能力强，计算简便的优点。

The existing methods for detecting bearing faults based on chaotic oscillators have been successfully applied. The key step of the method is to distinguish the phase transition of chaotic oscillators. Lyapunov exponents are usually used to judge the transformation, which is complicated and time-consuming. Starting with image recognition, an identification method based on polar radius invariant moment parameter for phase transformation was proposed. The Duffing chaotic oscillator was constructed, and the relationship between the phase transition and the cyclic dynamic force was analyzed, and the feasibility of the early fault identification for the bearing by chaotic oscillators was proved. Then, the definition of polar radius invariant moment was given, and it was proved that the value of performance was monotonically increasing in the process of chaotic oscillator phase transition from chaos to large-scale periodic state with the periodic perturbation increasing. The anti noise capability of polar radius invariant moments was discussed and compared with the HU's invariant moments and the two-dimensional approximate entropy method. Finally, the method was applied to the test of the early fault diagnosis in the power head bearing of drilling machine. The experimental results show that the polar radius invariant moment could identify the phase transition of chaotic oscillator, and the minimum detection signal-to-noise ratio was -36.99 dB, and the accuracy of recognition was improved by 4%-7% comparing with the other two methods. The method proposed can be used in early identification of bearing faults and has the advantages of high recognition accuracy, strong noise immunity and simple calculation.