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）.

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.

NONLINEAR MODELING AND CONTROLLING OF ARTIFICIAL MUSCLE SYSTEM USING NEURAL NETWORKS

The pneumatic artificial muscles are widely used in the fields of medicalrobots, etc. Neural networks are applied to modeling and controlling of artificial muscle system. Asingle-joint artificial muscle test system is designed. The recursive prediction error (RPE)algorithm which yields faster convergence than back propagation (BP) algorithm is applied to trainthe neural networks. The realization of RPE algorithm is given. The difference of modeling ofartificial muscles using neural networks with different input nodes and different hidden layer nodesis discussed. On this basis the nonlinear control scheme using neural networks for artificialmuscle system has been introduced. The experimental results show that the nonlinear control schemeyields faster response and higher control accuracy than the traditional linear control scheme.

Geometric Properties of AR(q) Nonlinear Regression Models

This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988)[1.2] and Seber & Wild (1989)[3].

A Gauss-Newton Approach for Nonlinear Optimal Control Problem with Model-Reality Differences

Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real plant. In this paper, a least squares scheme, which is based on the Gauss-Newton algorithm, is proposed. The aim is to approximate the output that is measured from the real plant. In doing so, an appropriate output measurement from the model used is suggested. During the computation procedure, the control trajectory is updated iteratively by using the Gauss-Newton recursion scheme. Consequently, the output residual between the original output and the suggested output is minimized. Here, the linear model-based optimal control model is considered, so as the optimal control law is constructed. By feed backing the updated control trajectory into the dynamic system, the iterative solution of the model used could approximate to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, current converted and isothermal reaction rector problems are studied and the results are demonstrated. In conclusion, the efficiency of the approach proposed is highly presented.

Nonlinear Systems Identification via an Input-Output Model Based on a Feedforward Neural Network

This paper develops a feedforward neural network based input output model for a general unknown nonlinear dynamic system identification when only the inputs and outputs are accessible observations. In the developed model, the size of the input space is directly related to the system order. By monitoring the identification error characteristic curve, we are able to determine the system order and subsequently an appropriate network structure for systems identification. Simulation results are promising and show that generic nonlinear systems can be identified, different cases of the same system can also be discriminated by our model.

Discrete-Time Nonlinear Stochastic Optimal Control Problem Based on Stochastic Approximation Approach

In this paper, a computational approach is proposed for solving the discrete-time nonlinear optimal control problem, which is disturbed by a sequence of random noises. Because of the exact solution of such optimal control problem is impossible to be obtained, estimating the state dynamics is currently required. Here, it is assumed that the output can be measured from the real plant process. In our approach, the state mean propagation is applied in order to construct a linear model-based optimal control problem, where the model output is measureable. On this basis, an output error, which takes into account the differences between the real output and the model output, is defined. Then, this output error is minimized by applying the stochastic approximation approach. During the computation procedure, the stochastic gradient is established, so as the optimal solution of the model used can be updated iteratively. Once the convergence is achieved, the iterative solution approximates to the true optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, an example on a continuous stirred-tank reactor problem is studied, and the result obtained shows the applicability of the approach proposed. Hence, the efficiency of the approach proposed is highly recommended.

双参数非线性概率模型的板材腐蚀精度估计

针对金属板腐蚀在线超声动态检测时探头抖动致使超声波入射角变化,引起测量精度低的问题,建立双参数超声波水浸检测误差修正的非线性概率模型,结合函数逼近理论补偿超声入射角引入误差。采用基函数加权组合与三阶拉格朗日插值结合方法,同时对超声波入射角、界面声程双参数与工件声程的函数关系进行最小二乘曲线拟合,得出入射角与检测误差的非线性相关关系。通过对误差补偿算法中非线性概率模型入射角与界面声程变量的迭代运算,利用折射角反向求解入射角,解决检测中超声波入射角不确定问题。在水层厚度30~45 mm范围内,对不同厚度铝板进行检测,结果表明,经模型补偿处理,超声波以0°~8°角入射,板材检测精度为1%,为有效提高腐蚀精度估计提供依据。

谐波减速器动力学特性与建模研究进展

谐波减速器具有相对质量低、结构紧和价格低廉等优点,广泛应用于空间机械臂关节设计.然而,谐波减速器的运动误差、刚度和摩擦3种动力学特性阻碍了空间机械臂关节指向精度、运动稳定度等性能指标的提升.为改善空间机械臂关节性能,国内外学者针对谐波减速器的运动误差、刚度和摩擦3种动力学特性开展了试验研究和机理分析,并建立了数学模型.本文从试验、机理和建模3个角度出发,系统论述关于谐波减速器的运动误差、刚度和摩擦3种动力学特性的最新研究成果,总结分析谐波减速器动力学特性和建模研究所面临的挑战以及未来发展的方向.

扩散硅压阻式压力传感器非线性误差纠正方法

针对扩散硅压阻式压力传感器非线性误差纠正易受到误差传递算法的影响,导致纠正后最大相对波动较高的问题,本文提出基于恢复函数的压力传感器非线性误差纠正方法。采集扩散硅压阻式压力传感器信号数据,去除噪音信号,以恢复函数为基础,设计传感器的非线性误差传递算法;利用支持向量机算法构建非线性误差校正模型,再通过遗传算法优化模型参数,实现误差的良好补偿。实验结果表明:本文所提出的纠正方法应用效果与文献相比,传感器的最大相对波动分别降低了13.53%与7.08%,具有更优的应用性能,值得推广。

基于模块化贝叶斯推理的随机非线性模型修正

为同时考虑多种不确定因素对非线性结构模型修正的影响,提出了一种基于模块化贝叶斯推理的随机非线性模型修正方法。为了描述具有时变特性的非线性动力响应,提取结构动力响应主分量的瞬时加速度幅值作为非线性指标,基于贝叶斯方法,将整个模型修正过程分为3个相互独立的模块:首先建立非线性模型的高斯过程替代模型记为模块一;同时,为考虑模型误差对非线性结构随机模型修正的影响,将设计变量作为输入,模型误差作为输出,建立关于模型误差的高斯过程替代模型,记为模块二;最后,结合贝叶斯推理方法与模块一和模块二中的高斯过程模型,利用过渡马尔可夫链蒙特卡罗(transitional Markov Chain Monte Carlo,TMCMC)随机采样方法估计待修正参数后验概率密度函数,实现基于模块化贝叶斯推理的随机非线性模型修正研究。采用三跨连续梁桥数值算例来验证所提出的随机非线性模型修正方法的准确性,并对比了不同噪声水平、不同程度模型误差条件下的模型修正结果。研究结果表明,基于模块化贝叶斯推理的随机非线性模型修正方法能够有效地实现非线性结构的随机模型修正,并具有较好的鲁棒性。

GNSS-A水下定位的动态非线性Gauss-Helmert模型及其抗差总体卡尔曼滤波算法

GNSS-声学组合式观测是确定海底控制点位置的重要手段,但会受到声速不确定性、海面平台定位偏差等误差因素的干扰,而基于误差传播定律的常规方法对各类误差的处理策略使得海底点坐标解算不准确。针对这一问题,本文将声速测距误差非时变项设为待解参数,在水下观测方程的系数矩阵中讨论声速测距误差时变项与换能器位置误差的影响,构建了GNSS-声学水下定位的动态非线性高斯-赫尔默特(Gauss-Helmert, GH)模型,并推导了该模型的总体卡尔曼滤波解。在此基础上,进一步考虑扩展后的观测信息受到粗差污染的情况,给出了模型的抗差处理方法及解算步骤。最后分别通过仿真试验和胶州湾海域实测试验进行了验证,试验结果表明,在不同深度或不同换能器位置误差大小的无粗差设定下,本文方法解算精度及稳定性较常规方法均更高;当观测信息含有粗差时,模型的抗差滤波算法能更准确地识别及定位异常信息,其三维点位精度明显更优,解算效果达到最佳。

伺服加载系统非线性建模及间隙补偿控制研究

分析机械间隙误差对于伺服加载系统加载液压缸位移、负载压力和流量的影响,提出了伺服加载系统机械间隙误差的补偿控制方法,建立了机械间隙误差影响下的伺服加载系统非线性模型。通过Simulink系统仿真和系统实验,对伺服加载系统非线性模型和机械间隙补偿方法的精确性进行验证。实验结果显示:低航速小负载工况时的输出负载力精度误差由18%降低至10%,高航速大负载工况时的输出负载力精度误差由21%降低至8%,被测产品伺服机构在全行程内的输出负载力滞后误差基本消除。

基于LabVIEW FPGA的压电迟滞补偿控制研究

对压电陶瓷驱动器在工作过程中因迟滞非线性效应造成的误差提出了一种迟滞误差补偿控制方法。首先针对迟滞非线性,基于PI模型构建了相应的迟滞模型,并利用其逆模型对压电驱动器的输入电压进行调整;其次针对PI模型的不足之处,结合PID闭环控制进一步对迟滞误差进行补偿。最后基于LabVIEW FPGA模块搭建了压电迟滞补偿控制系统,并进行了单轴正弦振动轨迹控制试验研究。试验结果表明,在复合控制下,压电陶瓷驱动器在100 Hz以内频率下输出位移的最大相对误差在3%以内。

Efficient Statistical Inference for Partially Nonlinear Errors-in-Variables Models

In this paper, we consider the partially nonlinear errors-in-variables models when the non- parametric component is measured with additive error. The profile nonlinear least squares estimator of unknown parameter and the estimator of nonparametric component are constructed, and their asymptotic properties are derived under general assumptions. Finite sample performances of the proposed statistical inference procedures are illustrated by Monte Carlo simulation studies.

The rate of convergence for the least squares estimator in nonlinear regression model with dependent errors

We study the parameter estimation in a nonlinear regression model with a general error's structure,strong consistency and strong consistency rate of the least squares estimator are obtained.

广东主要森林类型林分生物量和碳储量模型研建

【目的】构建广东省主要森林类型林分生物量和碳储量模型,为省内储量数据的本底摸查、省级与县市级储量数据的有效衔接提供模型支撑;分析树种结构和气候条件对模型的影响和作用机制,为更精细的碳汇监测及森林质量提升提供理论指导。【方法】以广东省12种主要森林类型为研究对象,基于2007、2012和2017年3期森林资源连续清查数据,采用非线性误差变量联立方程组构建各森林类型与蓄积量兼容的地上和地下生物量、地上和地下碳储量模型。以哑变量形式区分树种结构,以再参数化方法建立气候敏感的林分生物量和碳储量模型,评价模型拟合结果,分析气候变量对林分生物量和碳储量的影响。【结果】研究得到各森林类型的蓄积量、地上和地下生物量模型以及地上R^(2)_(a)和地下林分平均含碳系数。(1)基于胸高断面积和平均树高的基础模型调整决定系数()为0.947~0.997,总相对误差(TRE)和平均系统误差(MSE)分别在±1.54%和±2.48%范围,均不超±3%。平均预估误差(MPE)为0.30%~3.61%,仅栎树林、相思林部分模型略超3%。平均百分标准误差(MPSE)为3.30%~13.39%,均不超15%。(2)基于胸高断面积的简化模R^(2)_(a)型为0.876~0.996,除相思林地下生物量模型拟合效果较差外,其余模型的TRE和MSE分别在±3.19%和±2.74%范围,R^(2)_(a)MPE为0.36%~4.70%,MPSE为4.18%~15.61%。基于平均胸径和林分密度的补充模型为0.775~0.977,多数在0.9以上,除相思林部分模型拟合效果较差外,其余模型的TRE和MSE分别在±2.28%和±1.83%范围,MPE为1.12%~6.24%,R^(2)_(a)MPSE为5.91%~17.44%。(3)区分树种结构的林分模型为0.960~0.997,TRE和MSE分别在±1.61%和±2.33%范围,MPE为0.30%~3.41%,MPSE为2.67%~12.92%,多数模型显著优于基础模型。(4)建立8种森林类型气候敏感的林分生R^(2)_(a)物量和碳储量模型,为0.947~0.998,TRE和MSE分别在±1.86%和±1.96%范围,MPE为0.29%~2.65%,MPSE为3.18%~13.29%,多数模型较基础模型得到显著改进。生物量大多情况下与温度呈负相关,与蒸散量呈负相关或与降水量呈正相关。【结论】所建模型具有较好拟合效果和较高预估精度,实际应用时可根据数据详略和估算范围选择合适模型。温度过高、蒸散过多或降水不足是限制广东省森林生物量和碳储量增长的主要因素。

含有建模和测量误差的卫星自主定轨系统能观性分析

影响卫星自主轨道确定精度的主要因素包括动力学建模误差及测量误差。考虑动力学模型及测量均存在系统误差时,解决问题的一个途径是将这两种系统误差与卫星运动状态构成扩增状态后一同估计。为了保证滤波的稳定,就必须对此扩增系统的能观性进行分析。基于非线性系统的局部弱能观性理论,分析并给出了无摄动条件下单星自主定轨系统中卫星运动状态、建模误差及测量误差均能观的充要条件,即当轨道为圆轨道时增广系统处处不能观,当轨道不为圆轨道时处处能观。最后通过仿真算例对结论进行了验证,仿真结果显示对于非圆轨道,当建模误差及测量误差均为常值或慢时变时,采用扩展卡尔曼滤波算法对增广系统的状态估计是有效的。

Robust output-feedback control for stochastic nonlinear systems with modeling errors

In this paper, the stabilization problem of a stochastic nonlinear system with modeling errors is considered. An augmented observer is first presented to counteract the unmeasurable states as well as modeling errors. An adaptive output feedback controller is designed such that all signals in the closed-loop system are bounded in probability and the output is regulated to the origin almost surely.

基于Buck-Boost变换器的无源性研究

Buck-Boost变换器在恒功率负载情况下可能会导致系统振荡,为保证系统稳定运行,文章采用端口受控的哈密顿模型设计一种新型无源复合控制器;首先利用正切函数改进非线性状态误差反馈控制,更新无源控制的内环控制器,获得期望电流值,进而提高的系统动态性能,减小静态误差;其次结合POPOV超稳定定理优化无源控制的外环控制器,保证无源控制在内部扰动或外部扰动情况下均能稳定输出;之后通过仿真将所设计的新型无源复合控制器与三种经典的无源控制方法比较得出:新型无源复合控制器不仅可以提高系统的抗干扰能力,还能解决超调与快速性无法协调的问题;最后利用实验平台验证文章所提算法的可实施性。