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<span style="font-size: 10.5pt; font-family: &quot;Times New Roman&quot;; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US">The use of support vector machine (SVM) for function approximation has increased over the past few years. Unfortunately, the practical use of SVM is limited because the quality of SVM models heavily depends on a proper setting of SVM hyper-parameters and SVM kernel parameters. Therefore, it is necessary to develop an automated, reliable, and relatively fast approach to determine the values of these parameters that lead to the lowest generalization error. This paper presents two SVM parameter optimization approaches, i.e. GA-SVM and PSO-SVM. Both of them adopt a objective function which is based on the leave-one-out cross-validation, and the SVM parameters are optimized by using GA (genetic algorithm) and PSO (</span><span style="font-size: 10.5pt; font-family: &quot;Times New Roman&quot;; mso-fareast-font-family: 宋体; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US">particle swarm optimization) respectively. From experiment results, it can be concluded that both approaches, especially PSO-SVM, can solve the problem of estimating the optimal SVM parameter settings at a reasonable computational cost. Further, we point out the importance of a proper population size for GA/PSO-SVM, and present the recommended population size for GA-SVM and PSO-SVM.</span>

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To intuitively analyze the absolute and relative stability of the forward and backward whirling modes of the high-speed magnetically suspended flywheel rotor with significant gyroscopic effects and bending modes, this paper presents a whirling modes stability criterion based on complex coefficient frequency characteristics method. Through variable reconstruction, the multipleinput multiple-output magnetically suspended rotor system is converted into a single-input single-output (SISO) system with complex coefficients. The stability equivalence of the systems before and after variable reconstruction has been proven. Based on this, the inherent relationships between the distribution of the closedloop poles of the complex coefficient SISO system and the whirling modes stability are revealed, and the Nyquist stability criterion is further extended by applying the argument principle. All of these lay the foundation for the whirling modes stability theorem, and then, their stability criterion is further developed. Simulation and experimental results prove the effectiveness and correctness of the presented criterion.Index Terms-Bending mode, characteristic locus method, complex coefficient frequency characteristics, gyroscopic effects, magnetically suspended flywheel (MSFW), stability criterion, whirling mode.