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Statistical analysis and clustering of discontinuities existing in rock mass are the basis of rock mass engineering stability analysis. Considering that the mechanical and hydraulic properties of discontinuities are affected by many factors such as occurrence, trace length, aperture, roughness, and filling state, a multi-parameter dominant grouping method of rock mass discontinuities based on principal component analysis is proposed. Firstly, the principal component analysis method is used to select the criterion of the dominant grouping and calculate the weight value of its participation in similarity measurement. Secondly, the global optimal initial clustering center of the fuzzy C-means clustering algorithm is searched using the annealing genetic algorithm. Lastly, the objective function is established by minimizing the weighted sum of the distance between the discontinuities to be grouped and the clustering center, achieving the dominant grouping of multi-parameter rock mass discontinuity. Two hundred artificial discontinuities are divided into dominant groups using the multi-parameter method and the results are compared with other methods. The results show that this method has higher grouping accuracy. The method is applied to the multi-parameter dominant grouping of the measured discontinuities of Huayang Tunnel of Chongqing Third Ring Expressway. The grouping results are reasonable and reliable, which further verifies that the proposed method has a significant engineering application value.

In the paper, the authors establish several integral inequalities of the Ostrowski type for s-logarithmically convex functions. These integral inequalities modify the conditions and correct errors in two main theorems of the paper [A. O. Akdemir and M. Tunç, Ostrowski type inequalities for s-logarithmically convex functions in the second sense with applications, Georgian Math. J.22 (2015), no. 1, 1–7]. [ABSTRACT FROM AUTHOR]

The paper analyzed causes of startup inrush current of three-phase PWM rectifier, researched influence of initial phase angle of grid electromotive force and initial phase angle of AC side voltage on startup current, and proposed a method to use output of phase-locked loop to control initial phase angle of the grid electromotive force, which can avoid big startup current of a phase when starting, so as to make difference of three-phase AC currents between each other be not vary much. The experimental results verify correctness of the theoretical analysis and validity of the method.

The paper analyzed working principle of permanent magnet linear motor with moving coil, gave mathematical model of permanent magnet linear motor with moving coil which is used to drive electro-hydraulic proportional valve, and built simulation model of the motor with Matlab/Simulink software. The simulation result showed that regulating time of step response of the motor is less than 30 ms when displacement instruction is 5 mm, which has good dynamic response characteristics of high-frequency.

The paper introduced a design of control circuit of proportional solenoid based on AT89S52 single-chip microcomputer. The circuit uses ADC circuit to convert collected analog signals into digital signals for further procession by AT89S51, and PWM signal output by AT89S51 to make proportional solenoid act after procession of power conversion circuit. The debugging and running results showed validity of the circuit.