Stochastic Load Simulation And Structural Dynamic Response Analysis Based On Wavelet Transform

Structural vibration problem is common in civil engineering. The main task of structural vibration analysis is to research structural reponse rules under dynamic load, namely the relationship among dynamic load, structure and structural response and is to provide basis for structural dynamic reliability design. Some dynamic loads not only change with time but also exhibit obvious stochastic property, so it will be more reasonable to consider them as stochastic process and analyze them with random vibration theory. How to describe the non-stationary property of stochastic dynamic load and consider it fully and accurately during the solving process of structural response has been a difficult issue for researchers, however, it has not been resolved well as yet.Wavelet transform is a good time-frequency analysis tool with outstanding advantage than Fourier transform. Wavelet transform is able to observe changes of signal in both time domain and frequency domain, provide time and frequency local characteristics of signals, and it is particularly suitable for non-stationary signal analysis. Based on above circumstances, wavelet transform theory is introduced into stochastic load analysis, stochastic load simulation and structural vibration analysis, and related researches have been conducted in this paper. The major contents and investigation results of dissertation are given as follows:(1) Based on the filtering wave characteristics of continuous wavelet transform, the relationship between wavelet coefficients and time-dependent PSD is set up in terms of energy, and a time-dependent PSD estimation method based on wavelet transform is presented in this paper. It overcomes the disadvantage of lack of time information in power spectral density based on Fourier transform estimation, and is helpful to understand deeply time-frequency characteristics of non-stationary random signal. The time-dependent PSD estimation method based on wavelet transform suggested here is also applicable to power spectrum estimation of stationary signal and consistent result with conventional Fourier transform estimation can be obtained.(2) Utilizing the orthogonality of orthogonal wavelet basis in different frequency bands, the relationship between wavelet coefficients of discrete wavelet transform and power spectral density is derived, and stationary stochastic load series based on given power spectrum is created using inverse wavelet transform. Furthermore, the method is extended to spatial related multipoint process and spatial correlation fluctuating wind field simulation is conducted. Analysis of examples indicates that simulated wind field is consistent well with given power spectral density and spatial correlation.(3) In the process of wavelet transform, down-sampling will cause some problems, such as numbers of wavelet coefficients reducing under larger scale, difficult in reflecting statistical characteristics, and loss of time information. Aiming at above instances, discrete stationary wavelet transform is introduced and the relationship between wavelet coefficients and time-dependent PSD is researched. Non-stationary stochastic process simulation method based on discrete stationary wavelet transform is established, with which, ground motion acceleration time history based on given time-dependent PSD is simulated. At the same time, the approach of adjusting and simulating non-stationary time history using given historical record is also researched. Adjusting and reconstructing wavelet coefficients in different frequency bands utilizing wavelet transform, and based on this, new sample time history can be created. In this way, time-frequency characteristics of original signal can be reserved well, and statistical characteristics of created samples are commonly consistent with target spectrum or characteristics of original signal.(4) Using wavelet transform, input load and structure response is decomposed into different frequency bands and analyzed, which extends original two-dimentional relation of time-amplitude or frequency-amplitude to three-dimentional relation of time-frequency-amplitude, and understanding of structural response rules is deepened. Example results show that the frequency band of fundamental frequency plays a primary role in structural response, the further a frequency band is away from fundamental frequency, the smaller contribution it will create to structural displacement response. This is different from current viewpoint that low frequency bands play a primary role in structural response.(5) According to the disadvantage of large calculation, an improved algorithm is presented and demonstated in this paper. The calculation results consistency of improved method with existing methods is demonstrated by analysis of numerical examples, and the calculation amount of improved method is reduced N times (N represents scale numbers of wavelet decomposition) than existing methods.(6) The method suggested in this paper is used in time-dependent PSD estimation of structural response. Based on first-excursion failure criterion, the dynamic reliability analysis of a reinforced concrete structure under earthquake action is carried out utilizing existing methods. The results show that estimated reliability according to stationary hypothesis is not always more conservative than that of non-stationary hypothesis, and it is more close to practice to estimate reliability according to non-stationary hypothesis.