This paper presents a non-intrusive solenoid valve fault diagnosis method, which adopts the eigenvalue extraction scheme and combines the time-frequency analysis and time-domain analysis of the current signal through the solenoid valve fault pattern recognition method. Specifically, the research group selected the solenoid valve driving end current value and its second-order change rate curve as the characteristic curve, and then it extracted the time-domain parameters and the corresponding frequency band energy of the second-order change rate as the characteristic value. Then, the research group conducted time-frequency analysis on the basis of the current signal, created a multi-feature fusion feature vector and then input it into a multi-class support vector machine (SVM) for solenoid valve fault diagnosis. To evaluate the method, the research group developed a working solenoid valve model that integrated a magnetic circuit, circuit and spool motion, and the research group examined four typical solenoid valve states (normal, spring broken, spool stuck and spool slightly stuck), for which the research group collected the current signals during solenoid valve energization and closing. The trials involved analyzing the current characteristics of the drive end, both in simulation and experimental setups, and the research group demonstrated that the proposed drive end current detection diagnosis method can improve the accuracy of recognition by 15.22% compared with traditional neural network recognition methods. The SVM strategy exploiting a multi-feature fusion strategy can improve recognition accuracy by 8.7% and verification accuracy by 42.11% compared with SVM on the basis of the energy feature values.

Experimental modal analysis, dynamic modeling, and parameter identification were employed to investigate the flexible beam tire model for a heavy-loaded radial tire. The in-plane bending vibration of the flexible tread is researched with the flexible beam tire model. The coupled vibration equation of the flexible tread and continuous sidewall is modeled with a flexible beam on elastic continuous beam tire model. The nonlinear sidewall dynamics sensitive to the inflation pressure is obtained. The coupled modal features of a heavy-loaded radial tire are presented experimentally for different inflation pressures. Structural parameters are identified by a backward genetic algorithm based on the error between the experimental and analytical modal resonant frequency for different inflation pressures. Experimental and theoretical results show that the flexible beam on elastic continuous beam tire model developed for the heavy-loaded radial tire with a larger flat ratio can achieve higher precision in predicting the in-plane vibration modes of the heavy-loaded radial tire. It can be extended to analyze the vibration modes of the heavy-loaded radial tire with different inflation pressures by taking the inflation pressure-sensitive radial stiffness of the sidewall into consideration.

The modeling and vibration transfer function of in-plane rigid–elastic-coupled tire model is put forward for researching the heavy-loaded radial tire with the feather of larger radial length and width ratio. The coupled characteristic of tread and sidewall is taken into consideration, and the coupled natural frequencies are analyzed with the normal pressure and fixed rim. The rigid–elastic coupling equation is modeled with the flexible beam on elastic foundation, which tread is modeled as the Euler beam and the sidewall is regarded as the sub-sectional spring with lumped mass. The dynamic equation is discrete with finite difference method, and three-parameter rigid–elastic-coupled tire model is derived based on the geometrical and structural parameters. The structural parameters of the tire are identified by the genetic algorithm based on the experimental modal parameter of heavy-loaded tire, and the higher order modal frequency is predicted with the analytic method. The analytical transfer function between tread and tread, tread and sidewall is derived. Experimental and theoretical results show that the in-plane rigid–elastic-coupled tire model can achieve the higher precision on predicting the transfer function and vibration feature of heavy-loaded tire within the frequency band of 300 Hz, compared with the method which only considers the coupling of tread and rim and is limited to 180 Hz.