Dimension Reduction Simulation Of Stochastic Wind Velocity Field For Wind-resistance Dynamic Reliability Analysis Of High-rise Buildings

The stochastic wind-induced dynamic analysis plays a significant role on structural design for complex structures such as high-rise buildings and long-span bridges,while the rational depiction and simulation of stochastic wind loads acting on the structures serves as a critical step in stochastic dynamic analysis and reliability assessment of these complex engineering structures.Currently,the random simulation approaches related to the spectral representation method(SRM)and the proper orthogonal decomposition(POD)seem to be the most widely used approaches in the practices.However,the conventional SRM(C-SRM)and conventional POD(C-POD)essentially belong to the Monte Carlo simulation method.Theoretically,the efficiency of Monte Carlo methods is independent to the random variables characterizing the dimensions.However,almost all of the methods for pseudo-random numbers generation confront the challenges of the high-dimensional random variables.So it usually needs to generate a large number of wind samples to guarantee the accuracy of the simulation,leading to a huge computational cost for both the simulation of stochastic wind field and the dynamic responses analysis of structures based on the simulation processes.On the other hand,a complete probability set can't be obtained through the sample function set generated by conventional Monte Carlo simulation(CMCS)since the probability information of which is unknown,resulting in the wind-induced dynamic response analysis and wind-resistance reliability assessment are limited to the low-order statistical magnitude.Therefore,the present paper proposed a family of dimension reduction approaches(including the dimension reduction spectral representation method(DR-SRM)and the dimensional reduction proper orthogonal decomposition(DR-POD))in view of the dimension reduction of random variables for the purpose to bypass the above challenges that the CMCS faced.Firstly,in view of the Fourier-Stieltjes integral formula of stationary multivariate stochastic processes,a unified formulation accommodating spectral representation and proper orthogonal decomposition based on the orthogonal random variables was deduced.On this basis,the C-SRM and the C-POD based on the random phase angles were detailedly introduced,and the essential differences between the orthogonal-randomvariables-based representation formulas and the random-phase-angles-based simulation formulas were clarified as well.Secondly,a family of dimension reduction simulation approaches(including the DR-SRM and the DR-POD)were proposed by introducing the random function expression of orthogonal random variables with just 2 or 3 elementary random variables,and five different types of orthogonal random function were constructed to realize the dimension reduction representation of stationary multivariate stochastic processes.A satisfactory simulation accuracy could be guaranteed by generating just several hundreds of representative time histories since the representative point sets of elementary random variables were selected by the number-theoretic method.In order to illustrate the usefulness of the proposed approaches,two numerical examples were carried out to simulate the vertical stochastic wind velocity field of the high-rise buildings and the horizontal ergodic stochastic wind velocity field acting on the deck of a long-span bridge with different types of random functions.The accuracy of the simulation,efficiency,error convergence,ergonomics as well as robustness of the proposed approaches were significantly investigated through the comparison with the CMCS.Besides,the acceleration technique such as FFT algorithm was introduced to enhance the simulation efficiency of the proposed approaches.Thirdly,in the conjunction of the proposed approaches and the probability density evolution theory,the meticulous analysis of structural dynamic responses subjected to the stochastic wind loads and the wind-resistance reliability for a high-rise frame-shear wall structure was carried out.Since a complete probability set can be obtained by the proposed approach,the transmission and evolution of the probabilistic information from the load excitations to the structural dynamic responses of the structural dynamic system could be accurately depicted using the probability density evolution method.On this basis,the quantitative wind-resistance reliability of the frame-shear wall structure was accomplished by selecting the relative inter-storey displacement angle as the reliability index.The usefulness of the proposed approaches was further demonstrated in view of the engineering practices through the structural dynamic analysis.Finally,some concluding remarks and expectations of this paper were put forward.