Seismicity Non-stationary Characteristics Study Based On Wavelet Packet Transform

In the Civil Engineering, when the earthquake happens the structure response is under the influence of seismicity characteristics deeply. So it’s very necessary to know and understand the seismicity characteristics more in-depth. As a kind of dynamic input load, seismicity characteristics change with frequencies and times, so it appears obvious non-stationary properties. The non-stationary properties could have significant impacts on engineering vibration and the analysis of construction. Therefore, in the field of civil engineering structural anti-seismic, the study of seismicity non-stationary characteristics is always very hot. Meanwhile, giving the fact that seismicity happens rarely, it’s hard to find lots of statistical homogenous data which measured earthquake. And it’s unrealistic to use the measured sample datum fully for analysis as well. So, how to simulate the seismicity also needs to discuss.Compared with wavelet transform, wavelet packet transform is a more effective method to process seismic signals. Wavelet packet transform can not only provide partial characteristics of time domain and frequency domain, but also can get the subdivision of high frequencies, making up the shortages such as the wavelet transform’s poor resolution at high frequencies. Based on this, the article uses the theory of wavelet packet transform to analysis seismicity non-stationary characteristics analysis and ground motion simulations. The major contents and investigation conclusions are given as follows:Based on the target power spectrum, using the principle of independent weight in mathematical statistics, a method is proposed for selecting wavelet basis function in the simulation of seismic response spectrum from a quantitative point of view. Select the optimal wavelet base by comparing the quantitative indexes through an instance analysis using the method, and then contrast wave fitting spectrum based on the optimal base with the target spectrum to verify the correctness of this method.Make an analysis of the band alignment rules based on wavelet packet transform. Based on MATLAB platform, study the relationship between tree node numbers and band numbers with the aid of XOR algorithm. And then establish mutual transformation algorit hms between wavelet packet tree nodes and frequency bands. Choose Tangshan wave to make an instance analysis, and verify the correctness of the algorithms.Based on the theory of wavelet packet transform and the physical significance of the power spectrum, the relationship between the average power spectrum of sub-signal and the instantaneous power spectrum based on the wavelet packet transform definition is set up in terms of energy. And a time-dependent power spectrum estimation method is presented based on wavelet packet transform in this paper. In addition, from the physical significance, put time-dependent power spectrum in the degradation of time domain and frequency domain respectively, verified the correctness of the time-dependent power spectrum estimation.Based on the orthogonal characteristics of orthogonal wavelet basis during different frequency bands, the relationship between instantaneous power of the non-stationary seismicity sub-signal and the target time-dependent power spectrum is deduced in this paper. A simulation algorithm of non-stationary seismicity acceleration time history is set up using the inverse transformation of wavelet packet. Besides, based on given target time-dependent power spectrum and the simulation algorithm, seismicity acceleration time history is simulated. The numerical example shows that, simulation of time-dependent power spectrum matches better with the target time-dependent power spectrum, verified the correctness of this method.In the process of seismicity simulation, human factors involve in more and some unknown objective information may be missing. Considering the problems above, historical records of seismicity acceleration time history is adjusted based on the simulation algorithm above. Example analysis shows that the adjusted seismicity time history using the algorithm not only retains the characteristics of the original time history but also fits well with the target spectrum, being more suitable for engineering.