Random vibrations occur in many engineering systems including buildings subject to earthquake excitation, vehicles traveling on a rough road and off-shore platform in random waves. Analysis of random vibrations for linear systems has been well studied. For nonlinear systems, particularly for multi-degree-of-freedom systems, however, there are still many challenges including analyzing the probability distribution of transient responses of the system. Monte Carlo simulation was considered the only viable method for this task. In this paper, We propose a method to construct semi-analytical transient solutions of the probability distribution of transient responses of nonlinear systems by using the radial basis function neural networks. The activation functions consist of normalized Gaussian probability density functions. Two examples are presented to show the effectiveness of the proposed solution method. The transient probability distributions and response moments of these examples are presented, which have not been reported in the literature before.

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The inflow of the side pump sump is not smooth enough during the operation of a pumping station, resulting in an asymmetric adherent vortex that endangers the station's normal operation and safety. To solve this problem, flow field and vorticity distribution charts of different flow layers were created through the establishment of a numerical model of the pumping station inflow by means of the fluid simulation software. The formation mechanism of the asymmetric adherent vortex in the side pump sump was analysed by combining Reynolds shear stress distribution, the simplified Navier-Stokes equation, and the transport equation of turbulent kinetic energy. Furthermore, the accuracy of the numerical simulation results was verified using flow field data collected via particle image velocimetry at the junction of the forebay and pump sumps of the station. Results show that the distribution of inflow velocity is uneven due to the asymmetric friction of the inflow in the side pump sump. The transverse velocity formed from it generates the asymmetric vortex in the side pump sump and creates an inspiratory vortex.

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Abstract. An optimal sensor placement (OSP) method based on structural subsection technique (SST) and model reduction technique was proposed for modal identification of truss structures, which was conducted using genetic algorithm (GA). The constraints of GA variables were determined by SST in advance. Subsequently, according to model reduction technique, the optimal group of master degrees of freedom and the optimal objective function value were obtained using GA in a case of the given number of sensors. Correspondingly, the optimal number of sensors was determined according to optimal objective function values in cases of the different number of sensors. The proposed method was applied on a scaled jacket offshore platform to get its optimal number of sensors and the corresponding optimal sensor layout. Then modal kinetic energy and modal assurance criterion were adopted to evaluate vibration energy and mode independence property. The experiment was also conducted to verify the effectiveness of the selected optimal sensor layout. The results showed that experimental modes agreed reasonably well with numerical results. Moreover the influence of the proposed method using different optimal algorithms and model reduction technique on optimal results was also compared. The results showed that the influence was very little.