APPROXIMATE POWER OF HETEROSCEDASTICITY TEST IN NONLINEAR MODELS WITH ARIMA（0,1,0） ERRORS

This paper presents an approach for estimating power of the score test, based on an asymptotic approximation to the power of the score test under contiguous alternatives. The method is applied to the problem of power calculations for the score test of heteroscedasticity in European rabbit data （Ratkowsky, 1983）. Simulation studies are presented which indicate that the asymptotic approximation to the finite-sample situation is good over a wide range of parameter configurations.

Analytical exploration of γ-function explicit method for pseudodynamic testing of nonlinear systems

It has been well studied that the γ-function explicit method can be effective in providing favorable numerical dissipation for linear elastic systems. However, its performance for nonlinear systems is unclear due to a lack of analytical evaluation techniques. Thus, a novel technique is proposed herein to evaluate its efficiency for application to nonlinear systems by introducing two parameters to describe the stiffness change. As a result, the numerical properties and error propagation characteristics of the γ-function explicit method for the pseudodynamic testing of a nonlinear system are analytically assessed. It is found that the upper stability limit decreases as the step degree of nonlinearity increases; and it increases as the current degree of nonlinearity increases. It is also shown that this integration method provides favorable numerical dissipation not only for linear elastic systems but also for nonlinear systems. Furthermore, error propagation analysis reveals that the numerical dissipation can effectively suppress the severe error propagation of high frequency modes while the low frequency responses are almost unaffected for both linear elastic and nonlinear systems.

Optimal Budget Spending for Software Testing under the Condition of Nonlinear Constraint

Software testing is a very important phase of the software development process. It is a very difficult job for a software manager to allocate optimally the financial budget to a software project during testing. In this paper the problem of optimal allocation of the software testing cost is studied. There exist several models focused on the development of software costs measuring the number of software errors remaining in the software during testing. The purpose of this paper is to use these models to formulate the optimization problems of resource allocation: Minimization of the total number of software errors remaining in the system. On the assumption that a software project consists of some independent modules, the presented approach extends previous work by defining new goal functions and extending the primary assumption and precondition.

TESTING OF CORRELATION AND HETEROSCEDASTICITY IN NONLINEAR REGRESSION MODELS WITH DBL(p,q,1) RANDOM ERRORS

Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity （Kantz and Schreiber （1997））. Tsai （1986） introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR（1） errors. Liu （2003） introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL（p, 0, 1） errors. Therefore, the important problems in regression model axe detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL（p, q, 1） random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedasticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai （1986）, Wei, et al （1995）, and Liu, et al （2003）.

TESTING FOR VARYING DISPERSION OF LONGITUDINAL BINOMIAL DATA IN NONLINEAR LOGISTIC MODELS WITH RANDOM EFFECTS

In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)).

Nonlinear Modeling and Identification of Structural Joint by Response Control Vibration Test

Components of mechanical product are assembled by structural joints,such as bolting,riveting,welding,etc.Structural joints introduce nonlinearity to some engineering structures,and the nonlinearity need to be modeled precisely.To meet serious quality requirements,it is necessary to detect and identify nonlinearity of mechanical products for structural optimization.Modal test to acquire a dynamic response has been applied for decades,which provides reliable results for finite element(FE)model updating.Here response control vibration test for identification of nonlinearity is presented.A nonlinear system can be regarded as linearity for particular steady state response,and classical linear analysis tool is applicable to extract modal data for particular response.First,its applicability is illustrated by some numerical simulations.Subsequently,it is implemented on experimental setup with structural joints by shaking table.The stiffness and damping function dependent of relative displacement are fitted to describe its inherent nonlinearity.The spring and damping forces are identified by harmonic balance method(HBM)to predict output response.Based on the identified results,the procedure is recommended that it allows a reliable measurement of nonlinearity with a certain accuracy.

Calibration of Four Nonlinear Failure Envelopes from Triaxial Test Data and Influence of Nonlinearity on Geotechnical Computations

It is now recognized that many geomaterials have nonlinear failure envelopes. This non-linearity is most marked at lower stress levels, the failure envelope being of quasi-parabolic shape. It is not easy to calibrate these nonlinear failure envelopes from triaxial test data. Currently only the power-type failure envelope has been studied with an established formal procedure for its determination from triaxial test data. In this paper, a simplified procedure is evolved for the development of four different types of nonlinear envelopes. These are of invaluable assistance in the evaluation of true factors of safety in problems of slope stability and correct computation of lateral earth pressure and bearing capacity. The use of the Mohr-Coulomb failure envelopes leads to an overestimation of the factors of safety and other geotechnical quantities.

TESTING FOR VARYING DISPERSION IN DISCRETE EXPONENTIAL FAMILY NONLINEAR MODELS

It is necessary to test for varying dispersion in generalized nonlinear models.Wei,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models.This type of problem in the framework of general discrete exponential family nonlinear models is discussed.Two types of varying dispersion,which are random coefficients model and random effects model,are proposed,and corresponding score test statistics are constructed and expressed in simple,easy to use,matrix formulas.

通气孔对新型不锈钢芯管平压性能影响分析

不锈钢芯管作为不锈钢桥面芯板的重要传力构件,其平压力学性能与桥面板承载能力息息相关。因钎焊工艺要求,不锈钢芯管壁上开设有双通气圆孔。为研究双通气圆孔对不锈钢芯管平压性能的影响,开展2组不同厚度不锈钢芯管平压性能试验与有限元非线性屈曲分析。通过试验结果验证采用Riks弧长法进行不锈钢芯管非线性屈曲分析方法的正确性。并考虑圆孔直径d、偏心距e、芯管壁厚t等因素,建立不同规格不锈钢芯管模型,开展非线性屈曲分析,探究多参数协同作用下对不锈钢芯管平压性能的影响分析。研究结果表明:不锈钢芯管平压试验曲线表现出明显的非线性特征,分为弹性阶段、弹塑性阶段与塑性破坏阶段;通气孔、管端扳边处转角及管脚10 mm处易优先出现局部屈曲破坏;不锈钢芯管极限荷载Pu及其对应的压缩位移δ_(u)随孔径d、偏心距e的增加而减小,随壁厚t增加而增大;芯管极限荷载Pu受孔径d的影响大于受偏心距e的影响,增大孔径使芯管极限荷载Pu下降6.00%~15.51%,而增大偏心距使芯管极限荷载Pu下降0.64%~9.22%,芯管应规避在管身中部(e/H=0.5)开孔;当孔径比d/D≯0.04、偏心比e/H≯0.3时,通气孔对芯管极限承载力影响较小,对极限荷载下的压缩位移δ_(u)不产生影响,建议将其作为通气孔设计取值。研究中获得的临界值及变化规律可用于新型不锈钢桥面芯板结构设计与优化研究。

基于扩张状态观测器的伺服加载模糊滑模控制

针对电动伺服加载测试台存在的间隙、摩擦等非线性控制问题,以滑模变结构控制(SMC)为主体进行了加载控制器设计。分析伺服加载测试台整体结构,提出一种基于扩张状态扰动观测器(ESO)的模糊滑模控制(FSMC)策略。该策略在使用ESO针对伺服加载系统的外部干扰进行观测的基础上,设计了模糊控制对滑动模态面和滑模趋近律进行自适应调节,提高了系统的动态实时跟随能力和干扰补偿能力,并减小SMC控制器稳定时的抖振现象。仿真结果表明:所设计的基于扩张状态观测器的模糊滑模控制器(FSMC-ESO)对比传统SMC及PID控制具有更好的快速响应性和鲁棒性。

煤岩蠕变试验及其灾变模型

为全面揭示煤岩长历时蠕变破坏机制,开展了长历时煤岩单轴压缩分级蠕变声发射试验,分析了不同应力水平下煤岩蠕变变形和声发射规律,在此基础上,把临界幂律灾变函数引入理想黏弹塑性体,并与Burgers体串联,建立煤岩灾变蠕变模型。结果表明:煤岩单轴蠕变经历减速、稳定和加速蠕变3个阶段,声发射参数的变化规律能很好地反映煤岩蠕变3个阶段的变形特征;减速蠕变阶段内声发射事件较活跃,稳定蠕变阶段内低应力水平下声发射活动比中应力水平多,当从稳定蠕变阶段到加速蠕变阶段时,煤岩突然宏观脆性破坏,应变发生突变,声发射突然增大,呈现灾变破坏特征;高应力水平下的减速和稳定蠕变阶段煤岩内部裂隙充分且均匀发育,最终导致煤岩发生粉碎性的灾变破坏,这一破坏特征不同于单轴压缩破坏的剪切破坏;煤岩灾变蠕变模型能全面体现煤岩减速、稳定和加速蠕变阶段,已有几种非线性蠕变模型预测高应力水平蠕变试验结果相关系数最大为0.74,而灾变蠕变模型预测的相关系数大于0.97。岩石蠕变试验数据拟合结果表明灾变模型能够很好地描述各类岩石蠕变过程,临界幂律指数β对灾变破坏起控制作用,随着β的不断增大,岩石蠕变也从渐进式破坏转变为灾变破坏,从而验证了此煤岩灾变蠕变模型的正确性和适用性。

钢-混组合结构群钉连接件的连杆效应试验研究

钢—混组合结构连接件中栓钉式群钉连接件存在单钉承载力折减及群钉中栓钉的剪力分布不均匀的情况,本文提出一种带连杆的群钉连接件,旨在通过在栓钉之间设置连杆使群钉中栓钉之间的剪力分布更加均匀,并提高构件的整体承载能力。利用推出试验结合有限元模拟,揭示了带连杆群钉连接件的作用机理,并通过参数分析给出群钉构件合理的连杆布置位置以及尺寸。研究结果表明:在构件达到极限承载力时,合理的设置连杆能够减少83.76%的栓钉底部剪力分布的不均匀程度,对构件承载能力的提升能达到8.56%。本文研究可为带连杆群钉连接件的结构优化提供一定的理论基础,推动新型连接件的发展。

调谐惯质阻尼器动力试验和参数识别

研发了一种新型调谐惯质阻尼器(TVMD)装置,该装置分别采用电涡流与金属弹簧作为TVMD的阻尼元件与弹簧元件.首先,对该TVMD装置进行动力试验,研究其动力特性.然后,提出4种基于试验数据识别TVMD参数的方法,即峰值点拟合法、滞回曲线拟合法、时程拟合法和传递函数拟合法.动力试验结果表明:TVMD具有惯性质量放大效应和阻尼增益效应;弹簧元件和惯容元件均表现出理想的线性特性,而阻尼元件由于电涡流阻尼固有属性和TVMD装置中存在的摩擦,表现出非线性特性.参数识别结果表明:4种方法均能合理确定TVMD参数,其中,传递函数拟合法能提供用于调谐设计的等效阻尼系数,而其他3种方法能识别非线性阻尼模型的参数;滞回曲线拟合法和时程拟合法具有更高的参数识别精度,而峰值点拟合法和传递函数拟合法具有更高的计算效率.

采用多元非线性回归模型的无头铆钉安装干涉量预测

为明晰被连接件材料性能对安装干涉量的影响规律,并进一步为新材料扩展应用提供可靠性预测,在铆接过程有限元仿真数据基础上,提出了一种采用多元非线性回归模型的无头铆钉安装干涉量预测方法。首先,根据实际铆接过程建立有限元仿真模型,通过铆接试验验证模型有效性。然后,采用有限元和正交试验法,研究了被连接件弹性模量、屈服强度、强化系数和应变强度指数及其交互作用对铆接干涉量水平的显著性,明确了各因素对安装干涉量的影响效果。最后,选用幂函数作为多元非线性回归的函数形式,剔除显著性较低因素项,建立了待测位置干涉量回归预测模型。结果表明,在一定铆接工艺条件下,屈服强度和应变强度指数及其交互作用是影响干涉量水平的主要因素。对比模拟值与回归模型预测值发现两者变化趋势一致,且误差不超过10%,表明干涉量多元回归预测模型具有有效性。

中国空间站松不脱螺栓锁紧隔振器频率漂移建模与试验

中国空间站(以下简称空间站)大量科学仪器设备需要松不脱螺栓锁紧。针对空间站主动隔振器研制过程中松不脱螺栓锁紧诱发的频率漂移问题,探索了空间站主动隔振器锁紧状态非线性连接动力学机理建模与试验验证。对基于松不脱螺栓的隔振器锁紧释放装置进行力学分析,并根据松不脱螺栓接触面应力的非线性分布建立基于Iwan模型的系统等效动力学模型,分析动力学响应的非线性特性。研制空间站主动隔振器样机进行正弦振动试验,验证所建立动力学模型的准确性和有效性,为空间站精密科学设备环境适应性设计提供参考。

泥炭质土非线性固结理论研究

在泥炭质土软基固结过程中,孔隙比和渗透系数会随固结时间增加逐渐变小,导致按Terzaghi一维固结理论计算的软基固结值与实测值存在较大误差,故以滇池湖相沉积泥炭质土为研究对象,进行固结-渗透联合试验,研究泥炭质土e-σ′,k-σ′之间规律,从而得到e-lgσ′,lgk-lgσ′模型,然后引入这两个模型推导出适用于泥炭质土的一维非线性固结理论,并求解出渗压指数C_(k)=1,C_(k)=2两种不同条件下的解析解。根据所取泥炭质土的C_(k)不同,当C_(k)=1时,一维非线性固结微分方程的解析解与Terzaghi一维固结方程解析解比较,仅竖向固结系数存在差异;当C_(k)=2时,一维非线性固结微分方程难以直接得到解析解,可引入激活函数得到非线性固结微分方程的一个特解。研究发现,C_(k)=1时,泥炭质土固结过程中Terzaghi一维固结理论预测沉降速率比实测快,固结完成所需时间短;推导的一维非线性固结理论预测的各时间段固结沉降值和实测值接近,预测固结完成所需的时间误差小,且上覆荷载越大St-t关系曲线与实测值越接近,推导的一维非线性固结理论预测结果越精确。研究结果可为泥炭质土类软基提供一种更为精确的固结计算方法。

基于正余弦的非线性哈里斯鹰优化算法

针对哈里斯鹰优化算法(HHO)收敛精度低、易陷入局部最优等问题,提出了一种基于正余弦的非线性哈里斯鹰优化算法(SCNHHO)。首先,采用佳点集策略对种群进行初始化,使种群分布更均匀,提高算法收敛速度和精度;其次,在探索阶段引入正余弦策略,利用正余弦函数的震荡特性扩大搜索范围,寻求更多潜在的优质解;最后,在开发阶段引入非线性参数来平衡探索与开发,避免算法陷入局部最优。针对不同维度的基准测试函数进行性能测试,结合Wilcoxon秩和检验与Friedman检验的结果,将该算法与其他5个对比算法进行分析。结果表明,改进算法性能较原始HHO算法有较大提升,并且优于斑马优化算法(ZOA)、鲸鱼优化算法(WOA)和2种哈里斯鹰算法的变体(MHHO和IHHO),验证了改进策略的有效性。最后通过三杆桁架设计问题进一步验证了SCNHHO的实用性。

非线性超声检测系统检测分辨力和灵敏度的确定方法

为了提高非线性超声技术的检测能力并优化试验设置,提出了一种非线性超声检测系统的检测分辨力及检测灵敏度的确定方法,并根据该方法搭建了试验系统。对同一材料不同厚度的试件进行相同条件下的非线性超声二次谐波法检测,之后将测得的相对非线性系数与试件厚度进行线性拟合。拟合直线的斜率截距之比可表征该检测系统的检测分辨力,拟合直线的斜率可表征检测灵敏度。结果表明,该方法可去除非线性超声检测中的系统非线性,使测量数据具有更高对比度,利于基于非线性超声技术的材料损伤程度判定、微观组织演化评定等工作的高效展开。

红层泥岩填料蠕变特性及分数阶五元件非线性蠕变模型研究

为揭示红层泥岩填料的蠕变力学特性,对甘肃红层泥岩填料开展分级加载三轴CU蠕变试验,分析不同含水率和偏应力水平下红层泥岩填料的轴向蠕变、蠕变速率、应力-应变等时曲线等蠕变特性。基于红层泥岩填料蠕变曲线特征分析,引入分数阶微积分,构建适用于甘肃红层泥岩填料的分数阶五元件非线性蠕变模型,并对模型参数进行辨识和分析。研究结果表明:甘肃红层泥岩填料存在明显的蠕变特性,呈非线性衰减蠕变,随含水率与偏应力水平增大,蠕变变形明显增大;应力-应变等时曲线呈现出非线性特征,存在明显拐点,甘肃红层泥岩填料的长期强度为瞬时强度的0.6~0.8;所构建的模型可以准确地描述甘肃红层泥岩填料的蠕变特性,对试验结果的拟合效果明显比Burgers和Merchant模型拟合效果好。