On the distance spectra of threshold graphs

Rolling bearing fault diagnosis based on RQA with STD and WOA-SVM

“…The graph shows a significant increase in the white part. Improperly chosen distance thresholds can significantly impact the macroscopic and microscopic structure of the recurrence diagram, making it impossible to characterize the system's dynamics [ 30 ] correctly. They can also lead to the loss of meaning of the recurrence parameters calculated by quantitative analysis based on the recurrence diagram [ 31 ].…”

Fault analysis of industrial robots based on self‐organised critical theory

“…Take 1‐axis of industrial robot as an example to briefly explain the analysis process: (i) Collect vibration signals of the stationary and moving of industrial robot 1‐axis under the normal condition of different position, intercept signal within 0–20 s and filtering, oscillograph are shown in Figs. 3 and 4 below. (ii) By statistical methods obtained the threshold [14, 15] range of vibration signals in normal state of industrial robots. That is to say, the industrial robots are in normal and fault of critical state, then the small disturbance will be amplified and extended to the whole system, and that we said ‘self‐organised critical state’. (iii) Select the vibration signal of 1‐axis in the fault state and filter it, as shown in Fig.…”

Graphs with three distinct distance eigenvalues

“…For the former, Lu, Huang and Huang [23] determined all graphs whose distance matrices have exactly two eigenvalues (counting multiplicity) different from −1 and −3 and some other related results see [13,27]. Besides, the results in [24] and [22] stated that the multiplicities of distance eigenvalues −1 and −2 in a threshold graph (a graph contains no induced C 4 , P 4 or 2K 2 ) and a cograph (a graph contains no induced P 4 ), respectively. In general connected graphs, Li and Meng [18] characterized the graphs with certain multiplicity of the distance eigenvalue −2.…”