Research on the Fault Feature Extraction of Rolling Bearings Based on SGMD-CS and the AdaBoost Framework

Symplectic geometric mode decomposition (SGMD) is a newly proposed signal processing method. Because of its superiority, it has gained more and more attention in the field of fault diagnosis. However, the similar component reorganization problem involved in this method has not been clearly stated. Aiming at this problem, this paper proposes the SGMD-CS method based on the SGMD method and the cosine similarity (CS) and has been compared and verified on the simulation signal and the actual rolling bearing signal. In addition, in order to realize the intelligent diagnosis of the wind turbine bearing fault, the symplectic geometric entropy (SymEn) is extracted as the fault feature and input it into the AdaBoost classification model. In summary, this paper proposes a new wind turbine fault feature extraction method based on the SGMD-CS and AdaBoost framework, and the validity of the method is verified by the rolling bearing vibration data of the Electrical Engineering Laboratory of Case Western Reserve University.

Neither ancient nor modern: Wallis and Barrow on the composition of continua. Part one: Mathematical styles and the composition of continua

John Wallis and Isaac Barrow were key figures in a transitional period in the development of mathematics in early modern England: their work reveals a tension between the emerging algebraic techniques and the more traditional geometric mode of thought. Both men were among the first professional mathematicians in England. Wallis studied at Cambridge, deciphered Royalist codes for Parliament during the Civil War, and was one of the secretaries to the Assembly of Divines at Westminster. He was rewarded for his support of Parliament with the Savilian Professorship of Geometry at Oxford. Barrow was also a student at Cambridge and, in 1660, was appointed Regius Professor of Greek at Trinity College. He subsequently became Professor of Geometry at Gresham College, before finally becoming the Lucasian Professor of Mathematics at Cambridge. The work of both Wallis and Barrow was at the forefront of English mathematics in the second half of the seventeenth century. But even though both enjoyed very similar educations and careers, their mathematical techniques were quite different. Wallis’s style is usually considered algebraic, while Barrow’s is considered geometric. At the same time each man’s work exhibited a similar tension between tradition and innovation - between the mathematical ideas inherited from the Greeks and the demands of the new methods and problems.