正交Bent函数组与高非线性度满足SAC平衡函数

通过构造一组正交的Bent函数 (序列 ) ,利用它进一步构造出一类具有高非线性度、满足SAC的平衡函数 ,得到比较广泛的结果。

Time Dependent Gaussian Equivalent Linearization of Duffing Oscillator Using Continuous Wavelet Transform

Evolutionary response analysis of Duffing oscillator using Gaussian equivalent linearization in wavelet based time-frequency frame work is presented here. Cubic （i.e., odd type） non-linearity associated with stiffness and damping is modeled. The goal of this research is to develop the mathematical model of an equivalent linear system which is applicable for different non-stationary input processes （i.e., either summation of amplitude modulated stationary orthogonal processes or digitally simulated non-stationary processes）. The instantaneous parameters of the ELTVS （equivalent linear time varying system） are evaluated by minimizing the error between the displacements of non-linear and equivalent linear systems in wavelet domain. For this purpose, three different basis functions （i.e., Mexican Hat, Morlet and a modified form of Littlewood-Paley） are used. The unknown parameters （i.e., natural frequency and damping） of the ELTVS are optimized in stochastic least square sense. Numerical results are presented for different types of input to show the applicability and accuracy of the proposed wavelet based linearization technique.

Comparison of nonlinear and linear PCA on surface wind,surface height,and SST in the South China Sea

We compared nonlinear principal component analysis(NLPCA) with linear principal component analysis(LPCA) with the data of sea surface wind anomalies(SWA),surface height anomalies(SSHA),and sea surface temperature anomalies(SSTA),taken in the South China Sea(SCS) between 1993 and 2003.The SCS monthly data for SWA,SSHA and SSTA(i.e.,the anomalies with climatological seasonal cycle removed) were pre-filtered by LPCA,with only three leading modes retained.The first three modes of SWA,SSHA,and SSTA of LPCA explained 86%,71%,and 94% of the total variance in the original data,respectively.Thus,the three associated time coefficient functions(TCFs) were used as the input data for NLPCA network.The NLPCA was made based on feed-forward neural network models.Compared with classical linear PCA,the first NLPCA mode could explain more variance than linear PCA for the above data.The nonlinearity of SWA and SSHA were stronger in most areas of the SCS.The first mode of the NLPCA on the SWA and SSHA accounted for 67.26% of the variance versus 54.7%,and 60.24% versus 50.43%,respectively for the first LPCA mode.Conversely,the nonlinear SSTA,localized in the northern SCS and southern continental shelf region,resulted in little improvement in the explanation of the variance for the first NLPCA.

Crest-Height Distribution of Nonlinear Random Waves

The wave crest is an important factor for the design of both fixed and floating marine structures.Wave crest height is a dominant parameter in assessing the likelihood of wave-in-deck impact and resultant severe damage.Many empirical and theoretical distribution functions for wave crest heights have been proposed,but there is a lack of agreement between them.It is of significance to develop a better new nonlinear wave crest height distribution model.The progress in the research of wave crest heights is reviewed in this paper.Based on Stokes' wave theory,an approximate nonlinear wave crest-height distribution formula with simple parameters is derived.Two sets of measured data are presented and compared with various theoretical distributions of wave crests obtained from nonlinear wave models and analysis of the comparison is given in detail.The new crest-height distribution model agrees well with observations.Also,the new theoretical distribution is more accurate than the other methods cited in this paper and has a greater range of applications.

Study on seismic damage of SRHSC frame columns

The damage evolution in steel reinforced high strength concrete(SRHSC) frame columns was studied based on the test results of cyclic reversed loading experiment of 12 frame column specimens with various axial compression rations,stirrups ratios,steel rations and loading histories.The variation law of the ultimate bearing capacity,ultimate deformation and ultimate hysteretic energy dissipation of specimens under different loading protocols was obtained.The seismic damage characteristics,as well as strength and stiffness degradation,of SRHSC frame columns were analyzed.Based on the analysis of the nonlinear double parameters combination of deformation and energy,a damage model that can well reflect the mechanical characteristics of members subjected to a horizontal earthquake action was established by considering the effects of the number of the loading cycles on the ultimate resistance capacity(ultimate deformation and ultimate energy dissipation capacity) of members,and the loading history on damage,etc.According to the test results,the related parameters of the damage model were proposed.Finally,the damage model proposed was validated by the test results.Results indicated that the proposed damage model is theoretically more reasonable and can accurately describe the seismic damage evolution of the SRHSC frame columns.The results also can be used as a new theoretic reference for the establishment of damage-based earthquake-resistant design method of SRHSC members.

Effects of Higher-Order Relativistic Nonlinearity and Wakefield During a Moderately Intense Laser Pulse Propagation in a Plasma Channel

Using a variational approach,the propagation of a moderately intense laser pulse in a parabolic preformed plasma channel is investigated.The effects of higher-order relativistic nonlinearity (HRN) and wakefield are included.The effect of HRN serves as an additional defocusing mechanism and has the same order of magnitude in the spot size as that of the transverse wakefield (TWF).The effect of longitudinal wakefield is much larger than those of HRN and TWF for an intense laser pulse with the pulse length equaling the plasma wavelength.The catastrophic focusing of the laser spot size would be prevented in the present of HRN and then it varies with periodic focusing oscillations.