This paper consists of three parts. First, with a slightly-different, yet, more physically-plausible, discrete supply-rate (i.e. power), we propose a non-iterative (i.e. fast) and variable-step numerical integration algorithm for (scalar) discrete-passive mechanical systems, consisting of constant mass and damper, and a certain class of nonlinear spring. In the second part, we propose a fast passive collision handling algorithm with a spring-damper type virtual wall, which, to detect exact time of contacts, requires at most three intermediate non-iterative computations within each integration-step. We then propose a way of how to passively connect this discrete-passive, non-iterative, and variable-step mechanical integrators (with passive collision handling) to a continuous haptic device.

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With the rapid development of high-speed railways, fault detection and diagnosis for traction transformers are more and more important, and the detection method with high accuracy is the key to assure the normal operation of the traction power supply system. A method based on kernel principal component analysis (KPCA) and random forest (RF) is proposed to diagnose the traction transformer faults in this study. In this method, KPCA can obtain more fault characteristics in high-dimensional space through the non-linear transformation of the original data with dissolved gas analysis, and RF can utilise these characteristics to construct the classifier group. The experimental results show that the combination of KPCA and RF can effectively extract more characteristics of traction transformer faults to construct the classifiers with better performance, which contributes to the higher accuracy in traction transformer fault diagnosis and gets better anti-jamming performance.

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