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<p>In this study, the rotating shaft-two disk system with nonlinear supporting stiffnesses and an unbalanced concentrated mass is modeled. After obtaining the kinetic and potential energies of the rotating shaft system, the dynamic equations of the transverse vibration of the rotating shaft system are derived by using the improved <i>Fourier</i> series and the <i>Lagrange</i> equations of the second type. Then the fourth-order <i>Runge</i>–<i>Kutta</i> method is used to solve the system dynamic response for different initial values and nonlinear supporting stiffnesses. The amplitude-frequency characteristic curves of the system show the peak jumps, and the system phase diagram shows that the system is chaotic and other phenomena. The dynamic response provides 1,500,000 training sets and 1500 test sets. In this study, the error back propagation process of multi-hidden layer backpropagation (BP) neural network is derived in matrix form. The BP neural network obtained after using the same data 100 times in the training process has the highest recognition rate of nonlinear stiffness, which is 0.973. This BP neural network is applied for the first time to recognize the nonlinear stiffness of the rotating shaft system with different initial values, even if the dynamic response of the system is in an irregular chaotic state. It can be applied to the parameter identification and fault diagnosis of rotating machinery in practical engineering.</p>

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Application of BP neural network method to identify nonlinear translational stiffness in rotating shaft systems

  • 期刊论文

  • 发表日期：

    2026年1月28日

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  • Feifan He,
  • Jingtao Du,
  • Yang Liu,
  • Jingzhen Chen,
  • Jiayuan Tang

摘要

In this study, the rotating shaft-two disk system with nonlinear supporting stiffnesses and an unbalanced concentrated mass is modeled. After obtaining the kinetic and potential energies of the rotating shaft system, the dynamic equations of the transverse vibration of the rotating shaft system are derived by using the improved Fourier series and the Lagrange equations of the second type. Then the fourth-order Runge–Kutta method is used to solve the system dynamic response for different initial values and nonlinear supporting stiffnesses. The amplitude-frequency characteristic curves of the system show the peak jumps, and the system phase diagram shows that the system is chaotic and other phenomena. The dynamic response provides 1,500,000 training sets and 1500 test sets. In this study, the error back propagation process of multi-hidden layer backpropagation (BP) neural network is derived in matrix form. The BP neural network obtained after using the same data 100 times in the training process has the highest recognition rate of nonlinear stiffness, which is 0.973. This BP neural network is applied for the first time to recognize the nonlinear stiffness of the rotating shaft system with different initial values, even if the dynamic response of the system is in an irregular chaotic state. It can be applied to the parameter identification and fault diagnosis of rotating machinery in practical engineering.