In our previous work, a general particle filter based Bayesian method was proposed to derive the graphical relationship between wavelet parameters, including center frequency and bandwidth, and to posteriorly find optimal wavelet parameters so as to extract bearing fault features. In this work, some improvements on the previous Bayesian method are proposed. First, the previous Bayesian method strongly depended on an initial uniform distribution to generate random particles. Here, a random particle represented a potential solution to optimize wavelet parameters. Once the random particles were obtained, the previous Bayesian method could not generate new random particles. To solve this problem, this paper introduces Gaussian random walk to joint posterior probability density functions of wavelet parameters so that new random particles can be generated from Gaussian random walk to improve optimization of wavelet parameters. Besides, Gaussian random walk is automatically initialized by the famous fast kurtogram. Second, the previous work used the random particles generated from the initial uniform distribution to generate measurements. Because the random particles used in the previous work were fixed, the measurements were also fixed. To solve this problem, the first measurement used in this paper is provided by the fast kurtogram, and its linear extrapolations are used to generate monotonically increasing measurements. With the monotonically increasing measurements, optimization of wavelet parameters is further improved. At last, because Gaussian random walk is able to generate new random particles from joint posterior probability density functions of wavelet parameters, the number of the random particles is not necessarily set to a high value that was used in the previous work. Two instance studies were investigated to illustrate how the Gaussian random walk based Bayesian method works. Comparisons with the famous fast kurtogram were conducted to demonstrate that the Gaussian random walk based Bayesian method can better extract bearing fault features.

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