Dual time-delay Rényi entropy: a new wide-area information fusion and quantification method applied to intelligent fault diagnosis of rotating machinery

A new wide-area information fusion quantification method, dual time-delay Rényi entropy (DTDRE), is proposed to address the issue of the relatively high probability of faults in multi-stage planetary gear transmission systems under high-speed and heavy-load conditions. A state vector function with orthogonal relationships was proposed and a density matrix suitable for macroscopic non-linear systems was established, achieving data-level fusion of wide-area information. The application of DTDRE quantifies the information content, interaction relationship and correlation between different systems, solves the lifecycle monitoring problem of macroscopic non-linear systems and reveals the influence of time delay and fault characteristic information on the correlation between state vector functions. On this basis, an artificial intelligence diagnostic framework based on multivariate variational mode decomposition (MVMD), DTDRE and a deep residual network (DRN) was established. The experimental results show that the constructed intelligent learning framework can achieve accurate recognition of fault states and, compared with DenseNet and AlexNet, it has significant advantages in diagnostic accuracy and training stability.