Identification of nonlinear dynamic systems: Time-frequency filtering and skeleton curves

The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.

Identification of Nonlinear Systems Through Time-Frequency Filtering Technique

In the previous paper, a class of nonlinear system is mapped to a so-called skeleton linear model (SLM) based on the joint time-frequency analysis method. Behavior of the nonlinear system may be indicated quantitatively by the variance of the coefficients of SLM versus its response. Using this model we propose an identification method for nonlinear systems based on nonstationary vibration data in this paper. The key technique in the identification procedure is a time-frequency filtering method by which solution of the SLM is extracted from the response data of the corresponding nonlinear system. Two time-frequency filtering methods are discussed here. One is based on the quadratic time-frequency distribution and its inverse transform, the other is based on the quadratic time-frequency distribution and the wavelet transform. Both numerical examples and an experimental application are given to illustrate the validity of the technique.

Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

The joint time-frequency analysis method is adopted to study the nonlinear behavior varying with the instantaneous response for a class of S.D.O.F nonlinear system. A time-frequency masking operator, together with the conception of effective time-frequency region of the asymptotic signal are defined here. Based on these mathematical foundations, a so-called skeleton linear model (SLM) is constructed which has similar nonlinear characteristics with the nonlinear system. Two skeleton curves are deduced which can indicate the stiffness and damping in the nonlinear system. The relationship between the SLM and the nonlinear system, both parameters and solutions, is clarified. Based on this work a new identification technique of nonlinear systems using the nonstationary vibration data will be proposed through time-frequency filtering technique and wavelet transform in the following paper.

Comparison Between Lurr And State Vector Analysis Before Strong Earthquakes In Southern California Since 1980

There are seven strong earthquakes with M >= 6.5 that occurred in southern California during the period from 1980 to 2005. In this paper, these earthquakes were studied by the LURR (Load/Unload Response Ratio) method and the State Vector method to detect if there are anomalies before them. The results show that LURR anomalies appeared before 6 earthquakes out of 7 and State Vector anomalies appeared before all 7 earthquakes. For the LURR method, the interval between maximum LURR value and the forthcoming earthquake is 1 to 19 months, and the dominant mean interval is about 10.7 months. For the State Vector method, the interval between the maximum modulus of increment State Vector and the forthcoming earthquake is from 3 to 27 months, but the dominant mean interval between the occurrence time of the maximum State Vector anomaly and the forthcoming earthquake is about 4.7 months. The results also show that the minimum valid space window scale for the LURR and the State Vector is a circle with a radius of 100 km and a square of 3 degrees 3 degrees, respectively. These results imply that the State Vector method is more effective for short-term earthquake prediction than the LURR method, however the LURR method is more effective for location prediction than the State Vector method.

Experimental Study Of Vortex-Induced Vibrations Of A Cylinder Near A Rigid Plane Boundary In Steady Flow

In this study, the vortex-induced vibrations of a cylinder near a rigid plane boundary in a steady flow are studied experimentally. The phenomenon of vortex-induced vibrations of the cylinder near the rigid plane boundary is reproduced in the flume. The vortex shedding frequency and mode are also measured by the methods of hot film velocimeter and hydrogen bubbles. A parametric study is carried out to investigate the influences of reduced velocity, gap-to-diameter ratio, stability parameter and mass ratio on the amplitude and frequency responses of the cylinder. Experimental results indicate: (1) the Strouhal number (St) is around 0.2 for the stationary cylinder near a plane boundary in the sub-critical flow regime; (2) with increasing gap-to-diameter ratio (e (0)/D), the amplitude ratio (A/D) gets larger but frequency ratio (f/f (n) ) has a slight variation for the case of larger values of e (0)/D (e (0)/D > 0.66 in this study); (3) there is a clear difference of amplitude and frequency responses of the cylinder between the larger gap-to-diameter ratios (e (0)/D > 0.66) and the smaller ones (e (0)/D < 0.3); (4) the vibration of the cylinder is easier to occur and the range of vibration in terms of V (r) number becomes more extensive with decrease of the stability parameter, but the frequency response is affected slightly by the stability parameter; (5) with decreasing mass ratio, the width of the lock-in ranges in terms of V (r) and the frequency ratio (f/f (n) ) become larger.

2-DELTA-FUNCTION GENERALIZED PLASMA POLE MODEL FOR 1ST PRINCIPLE CALCULATIONS OF QUASI-PARTICLE ENERGIES IN MANY-ELECTRON SYSTEMS

To evaluate the dynamical effects of the screened interaction in the calculations of quasiparticle energies in many-electron systems a two-delta-function generalized plasma pole model (GPP) is introduced to simulate the dynamical dielectric function. The usual single delta-function GPP model has the drawback of over simplifications and for the crystals without the center of symmetry is inappropriate to describe the finite frequency behavior for dielectric function matrices. The discrete frequency summation method requires too much computation to achieve converged results since ab initio calculations of dielectric function matrices are to be carried out for many different frequencies. The two-delta GPP model is an optimization of the two approaches. We analyze the two-delta GPP model and propose a method to determine from the first principle calculations the amplitudes and effective frequencies of these delta-functions. Analytical solutions are found for the second order equations for the parameter matrices entering the model. This enables realistic applications of the method to the first principle quasiparticle calculations and makes the calculations truly adjustable parameter free.

加卸载响应比方法在结构灾变预测中的应用

加卸载响应比方法为非均匀脆性介质的灾变评估提供了新的思路,即用加载与卸载响应的差别来定量刻画介质的损伤程度.为了验证加卸载响应比方法应用于结构失效分析的有效性,首先运用加卸载响应比方法对意大利那不勒斯大学完成的1个2层楼房的加卸载实验进行分析,结果表明:在临近结构破坏之前加卸载响应比时间序列确实出现了异常明显的升高及回落;进而引入岩石破裂声发射实验进行研究,发现采用轴向应变做响应量计算得剑的加卸载响应比时间序列与楼房结构的响应比曲线在演化趋势上非常一致.进一步比较声发射能量率和宏观应做为响应得到的加卸载响应比时间序列,发现两者有着较为同步的稳定、异常、升高至峰值、急剧回落的演化过程.为了明确加卸载响应比与结构内部损伤的联系,基于损伤力学方法从理论上对此进行了分析,很明显加卸载响应比值在一定程度上可以反推结构的损伤程度,其演化可以为大型结构健康评估和工程灾变分析提供有益的参考及借鉴.

基于振幅稳定的原点反共振振动机动力学分析及其控制

利用反共振原理可有效减小振动机械对基础的作用,提高振动机械的寿命。建立了原点反共振振动机的动力学模型,阐明了其工作原理。以工作体和下质体振幅稳定为核心,分析了各系统参数一定时质量比和反共振频率比对系统振幅稳定性的影响情况,得到了作为组合参数时质量比和反共振频率比分别与上下质体动力放大因子的关系曲面,由此可得到满足工艺要求并能保证振幅稳定的参数区间,为各类反共振振动机设计提供了重要依据。研究了物料质量波动对系统振幅稳定性的影响和反共振点的漂移情况,揭示了对反共振机激振频率进行控制的必要性。在合理动力学参数组合的前提下通过引入控制技术,有效地提高了反共振振动机的工作机体和下质体的振幅稳定性。

小湾电站坝基岩体卸荷工程地质力学研究

Dam is the key main works in the construction of water power. The success or failure of the construction of the dam mainly depends on the stability of the dam foundation. The double curvature arch dam-XiaoWan Dam is the highest one among the dams with the same type in the world, and the water thrust acted on it reaches ton, so the rock bearing capacity of dam foundation becomes more important. Because of the high and steep valley-side slope, the large scale of excavation and the complex body type of excavation, it is prominent that the problem of stress release of the rock mass in dam foundation. More great attentions should be paid for the stability and the degraded of rock properties of rock mass induced by the stress release. In this paper, the phenomena of stress release of rock mass in XiaoWan Dam foundation and its mechanisms were analyzed based on the collection of data, the detailed field engineering investigations, measurement of the rock mass and the 2D numerical calculations. The rock mass under the foundation is weak-weathered to intact, the quality of which is good. After excavation of the foundation, the rock mass near the slope surface occurred extend, stretch and stick-slip along original textures till the new fracture surface formed. Then platy structure of the rock mass takes on. The rock mass in the dam foundation occur resilience due to stress release towards free faces with the characteristics of time effect and localized deformation. In-situ measurements show that the rock mass near the surface are degraded. The stress release induced by excavation is a process of the interaction between engineering structures and geologic body. The stress release of rock mass in dam foundation is related to the changed degree of geometrical conditions. The rock near excavation surface failed nearly under uniaxial stresses. The bending-breaking mechanism of plate girder can interpret the failure model of the rock mass with platy structure in dam foundation slope. In essence, the stress release is the change of stress field including the change of directions and magnitudes of stress induced by excavation, which can induce the comedown of the safety margin. In this paper, the inducing conditions of stress release were calculated by numerical analyses. Moreover, from the point of view that the change of stress field, the coefficient of K, i.e. the variable load coefficient was proposed. Then the law of the change of it is interpreted. The distributional characteristics of fracture zone were expressed by the coefficient. The stress release of hard rock has the characteristic of localization. The measuring technique of sound wave can not reflect the small cracks in this kind of rock mass due to stress release. So, the spectral analysis method was proposed. At the same time, the application foreground in engineering of the Stockwell Time-Frequency- Spectrum method was discussed with a view to the limitation of it.

利用分频与反演提高地震资料信噪比与分辨率方法研究

This thesis mainly talks about the wavelet transfrom and the frequency division method. It describes the frequency division processing on prestack or post-stack seismic data and application of inversion noise attenuation, frequency division residual static correction and high resolution data in reservoir inversion. This thesis not only describes the frequency division and inversion in theory, but also proves it by model calculation. All the methods are integrated together. The actual data processing demonstrates the applying results. This thesis analyzes the differences and limitation between t-x prediction filter and f-x prediction filter noise attenuation from wavelet transform theory. It considers that we can do the frequency division attenuation process of noise and signal by wavelet frequency division theory according to the differences of noise and signal in phase, amplitude and frequency. By comparison with the f-x coherence noise, removal method, it approves the effects and practicability of frequency division in coherence and random noise isolation. In order to solve the side effects in non-noise area, we: take the area constraint method and only apply the frequency division processing in the noise area. So it can solve the problem of low frequency loss in non-noise area. The residual moveout differences in seismic data processing have a great effect on stack image and resolutions. Different frequency components have different residual moveout differences. The frequency division residual static correction realizes the frequency division and the calculation of residual correction magnitude. It also solves the problems of different residual correction magnitude in different frequency and protects the high frequency information in data. By actual data processing, we can get good results in phase residual moveout differences elimination of pre-stack data, stack image quality and improvement of data resolution. This thesis analyses the characters of the random noises and its descriptions in time domain and frequency domain. Furthermore it gives the inversion prediction solution methods and realizes the frequency division inversion attenuation of the random noise. By the analysis of results of the actual data processing, we show that the noise removed by inversion has its own advantages. By analyzing parameter's about resolution and technology of high resolution data processing, this thesis describes the relations between frequency domain and resolution, parameters about resolution and methods to increase resolution. It also gives the processing flows of the high resolution data; the effect and influence of reservoir inversion caused by high resolution data. Finally it proves the accuracy and precision of the reservoir inversion results. The research results of this thesis reveal that frequency division noise attenuation, frequency residual correction and inversion noise attenuation are effective methods to increase the SNR and resolution of seismic data.

多波分量地震资料处理解释方法

To deal with some key problems in multi-component seismic exploration, some methods are introduced in this thesis based on reading amounts of papers about multi-component seismic theories and methods. First, to find a solution for the detection of the fracture density and orientation in igneous, carbonate and shale reservoirs, a large amount of which exist in domestic oil fields with low exploration and development degree, a new fast and slow shear waves separation method called Ratio Method based on S-wave splitting theory is discussed in this thesis, through which the anisotropy coefficient as well as fracture parameters such as density and azimuthal angle can be acquired. Another main point in this thesis involves the application of seismic velocity ratio (Vp/Vs) to predict the Hthological parameters of subsurface medium. To deal with the unfeasibility of velocity ratio calculation method based on time ratio due to the usually low single-noise ratio of S-wave seismic data acquired on land, a new method based on detailed velocity analysis is introduced. Third, pre-stack Kirchhoff integral migration is a new method developed in recent years, through which both S and P component seismic data as well as amplitude ratio of P/S waves can be acquired. In this thesis, the research on untilizing the P and S wave sections as well as amplitude ratio sections to interpret low-amplitude structures and lithological traps is carried out. The fast and slow shear wave separation method is then be applied respectively to detect the density and azimuthal angle of fractures in an igneous rock gas reservoir and the coal formation in a coal field. Two velocity ratio-calculating methods are applied respectively in the lithological prediction at the gas and coal field after summarizing a large amount of experimental results draw domestically and abroad. P and S wave sections as well as amplitude ratio sections are used to identify low-amplitude structures and lithological traps in the slope area of a oil-bearing sedimentary basin. The calculated data concerning fracture density and azimuthal angle through the introduced method matches well with the regional stress and actual drilling data. The predicted lithological data reflects the actual drilling data. Some of the low-amplitude and lithological traps determined by Kirchhoff migration method are verified by the actual drilling data. These results indicate that these methods are very meaningful when dealing with complex oil and gas reservoir, and can be applied in other areas.

品牌形象的消费行为学分析

Brand image is the attributes set and the related associations of a brand in consumers mind, and it is the subjective reflections of brands. The paper explored the factors of brand image system and their weight. As the traditional means to evaluate weight coefficients are not perfect, a new method, conjoint analysis, was attempted. The factors of brand image were explored through questionnaire. Sports sneaker, toothpaste, and personal stereo were chosen as product sample, and four hundred and twenty university students from Tangshan city and Beijing as subjects(each person evaluated two kinds of products). The first two kinds of products were requisites of students, and sports sneaker belonged to High conspicuous products and toothpaste was low conspicuous product. On the other hand, personal stereo was the sample of development and entertainment products. Several factors of three products brand were taken out with factor analysis. In order to explore the weight of the brand image factors, a contrast of factor contribution ratio method, holistic quartation method and conjoint analysis is made here. Twenty university students evaluated the weight of the image factors of three kinds of brand with holistic quartation method, then they gave the weight of personal stereo with conjoint analysis method. Product function, advertising and propaganda, symbolic meaning, market orientation, brand appetency, consuming experience are the factors of sports sneaker brand image. Product function, advertising and propaganda, market orientation, product grade, corporation image are the factors of toothpaste brand image. Corporation image and product function, advertising and propaganda, consuming experience, symbolic meaning, price and function ratio are the factors of personal stereo brand image. So the hypothesis was proved that brand image is an ordinal and organical system, "ordinal" means the weight of factors are different, "organical" means that brand image can be deposed into several factors and the factors belonged to function components and meaning components (function components are the factors about physical characteristics and function, which are called "hard factors"); meaning factors are those that can show the personality、value and lifestyle of consumers, which are called "soft factors". The research also gave evidence of the hypothesis below: the factor structures of brand image of different product category have commonness and individuality; the function components of low conspicuous products are more important than the high conspicuous products. The exploration of conjoint analysis is what the paper seeks to be some creative in some degree.

An Approximate Method For Calculation Of Fluid Force And Response Of A Circular Cylinder At Lock-In

In this paper, equations calculating lift force of a rigid circular cyclinder at lock-in uniform flow are deduced in detail. Besides, equations calculating the lift force on a long flexible circular cyclinder at lock-in are deduced based on mode analysis of a multi-degree freedom system. The simplified forms of these equations are also given. Furthermore, an approximate method to predict the forces and response of rigid circular cyclinders and long flexible circular cyclinders at lock-in is introduced in the case of low mass-damping ratio. A method to eliminate one deficiency of these equations is introduced. Comparison with experimental results show the effectiveness of this approximate method.