The variational mode decomposition (VMD) method for signal decomposition is severely affected by the number of components of the VMD method. In order to determine the decomposition modal number, K, in the VMD method, a new center frequency method of the multi-threshold is proposed in this paper. Then, an improved VMD (MTCFVMD) algorithm based on the center frequency method of the multi-threshold is obtained to decompose the vibration signal into a series of intrinsic modal functions (IMFs). The Hilbert transformation is used to calculate the envelope signal of each IMF component, and the maximum frequency value of the power spectral density is obtained in order to effectively and accurately extract the fault characteristic frequency and realize the fault diagnosis. The rolling element vibration data of the motor bearing is used to test the effectiveness of proposed methods. The experiment results show that the center frequency method of the multi-threshold can effectively determine the number, K, of decomposed modes. The proposed fault diagnosis method based on MTCFVMD and Hilbert transformation can effectively and accurately extract the fault characteristic frequency, rotation frequency, and frequency doubling, and can obtain higher diagnostic accuracy.

Some typical security algorithms such as SHA, MD4, MD5, etc. have been cracked in recent years. However, these algorithms have some shortcomings. Therefore, the traditional one-dimensional-mapping coupled lattice is improved by using the idea of polymorphism in this paper, and a polymorphic mapping–coupled map lattice with information entropy is developed for encrypting color images. Firstly, we extend a diffusion matrix with the original 4 × 4 matrix into an n × n matrix. Then, the Huffman idea is employed to propose a new pixel-level substitution method, which is applied to replace the grey degree value. We employ the idea of polymorphism and select f(x) in the spatiotemporal chaotic system. The pseudo-random sequence is more diversified and the sequence is homogenized. Finally, three plaintext color images of $256\times 256\times 3$, “Lena”, “Peppers” and “Mandrill”, are selected in order to prove the effectiveness of the proposed algorithm. The experimental results show that the proposed algorithm has a large key space, better sensitivity to keys and plaintext images, and a better encryption effect.