The recurrence plot (RP) method has been introduced into bearing fault diagnosis due to its capability of effectively analyzing nonlinear and non-stationary waveform signals in dynamic systems. However, the interference of noise increases the difficulty of RP-based fault diagnosis. To solve this problem, this paper proposed a novel anti-noise bearing fault diagnosis method based on improved RP and a convolutional neural network. First, different scales of approximation coefficients and detail coefficients were obtained and constructured for RP based on wavelet packet decomposition (WPD) on the vibrational signal. Meanwhile, redundant parts of each RP were removed according to its symmetry characteristics, and the remaining parts of these RPs were spliced into multi-scale asymmetric RP (MARP) containing all coefficients. Then, a fault diagnosis model for rolling bearing was established with MARP as the input of the pre-trained ResNet-34. Finally, the validity of the proposed fault diagnosis method was validated on the Paderborn bearing dataset. Experimental results showed that the proposed fault diagnosis method achieved an accuracy of 90% under Gaussian white noise with a signal-to-noise ratio of above -6 dB.

A multi-objective optimization method for the accelerated degradation test based on Wiener process is proposed in this article in order to solve the problem that a single objective optimization cannot solve the difficulty or even conflicting test configurations caused by different optimization objective functions. An accelerated degradation model is established based on Wiener process, and the unknown parameters are solved by a two-step maximum likelihood estimation method. Considering both the accuracies of life estimation and the model parameter estimation, a multi-objective optimization model is established with the optimization goals of the minimum asymptotic variance of P-quantile of lifetime and the maximum determinant of Fisher information matrix. The Pareto solutions are set by the multi-objective genetic algorithm, and the test configurations for multi-objectives are obtained. Under the step stress accelerated degradation test and the constant stress accelerated degradation test, the effectiveness of the proposed method is verified by an optimization example of LEDs accelerated degradation test.

Aiming at the multi-dimensional cognitive uncertainties in performance degradation modelling for small samples, a reliability assessment method is proposed based on uncertainty theory. First, a degradation model is established based on the uncertain process, which considers cognitive uncertainties from the time fluctuation, the measurement error, and the individual differences in initial value and degradation rate, and the reliability function is derived. Then, a two-step parameter estimation method for the degradation model is proposed based on the α-path and the least square, which is verified by numerical simulation. Finally, the effectiveness and superiority of the proposed method are verified by the cases of GaAs lasers and magneto-optic data storage disks, and parameter sensitivity analysis is conducted. The results indicate that uncertainty affects product reliability greatly. For small samples, the degradation models considering multi-dimensional uncertainties based on the Liu process has smaller fitting errors than that based on the Wiener process.