CONSERVATIVE ESTIMATING FUNCTION IN THE NONLINEAR REGRESSION MODEL WITH AGGREGATED DATA

The purpose of this paper is to study the theory of conservative estimating functions in nonlinear regression model with aggregated data. In this model, a quasi-score function with aggregated data is defined. When this function happens to be conservative, it is projection of the true score function onto a class of estimation functions. By constructing, the potential function for the projected score with aggregated data is obtained, which have some properties of log-likelihood function.

Heteroscedasticity check in nonlinear semiparametric models based on nonparametric variance function

The assumption of homoscedasticity has received much attention in classical analysis of regression. Heteroscedasticity tests have been well studied in parametric and nonparametric regressions. The aim of this paper is to present a test of heteroscedasticity for nonlinear semiparametric regression models with nonparametric variance function. The validity of the proposed test is illustrated by two simulated examples and a real data example.

Stability Analysis for a Discrete SIR Epidemic Model with Delay and General Nonlinear Incidence Function

In this paper, we construct a backward difference scheme for a class of SIR epidemic model with general incidence f . The step sizeτ used in our discretization is one. The dynamical properties are investigated (positivity and the boundedness of solution). By constructing the Lyapunov function, the general incidence function f must satisfy certain assumptions, under which, we establish the global stability of endemic equilibrium when R0 >1. The global stability of diseases-free equilibrium is also established when R0 ≤1. In addition we present numerical results of the continuous and discrete model of the different class according to the value of basic reproduction number R0.

Stability of a Delayed Stochastic Epidemic COVID-19 Model with Vaccination and with Differential Susceptibility

In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R0 ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.

Model tests and numerical analyses on horizontal impedance functions of inclined single piles embedded in cohesionless soil

Horizontal impedance functions of inclined single piles are measured experimentally for model soil-pile systems with both the effects of local soil nonlinearity and resonant characteristics.Two practical pile inclinations of 5掳 and 10掳 in addition to a vertical pile embedded in cohesionless soil and subjected to lateral harmonic pile head loadings for a wide range of frequencies are considered.Results obtained with low-to-high amplitude of lateral loadings on model soil-pile systems encased in a laminar shear box show that the local nonlinearities have a profound impact on the horizontal impedance functions of piles.Horizontal impedance functions of inclined piles are found to be smaller than the vertical pile and the values decrease as the angle of pile inclination increases.Distinct values of horizontal impedance functions are obtained for the ＇positive＇ and ＇negative＇ cycles of harmonic loadings,leading to asymmetric force-displacement relationships for the inclined piles.Validation of these experimental results is carried out through three-dimensional nonlinear finite element analyses,and the results from the numerical models are in good agreement with the experimental data.Sensitivity analyses conducted on the numerical models suggest that the consideration of local nonlinearity at the vicinity of the soil-pile interface influence the response of the soil-pile systems.

A Simplified Nonlinear Generalized Maxwell Model for Predicting the Time Dependent Behavior of Viscoelastic Materials

In this paper, a simple nonlinear Maxwell model consisting of a nonlinear spring connected in series with a nonlinear dashpot obeying a power-law with constant material parameters, for representing successfully the time-dependent properties of a variety of viscoelastic materials, is proposed. Numerical examples are performed to illustrate the sensitivity of the model to material parameters.

Resolution of Relationship between Organizational Performance and Human Resource Management through Nonlinear Modeling

The relation between the HRM and the firm performance is analyzed statistically by many researchers in the literature. However, there are very few nonlinear approaches in literature for finding the relation between Human Resource Management (FIRM) and firm performance. This paper exposes the relationship between human resource management and organizational performance through the use of nonlinear modeling technique. The modeling is proposed based on Radial Basis Function (RBF) which is nonlinear modeling technique in literature. The relation between 12 input and 9 output parameters is investigated in this research that is collected between 54 companies in Turkey which indicated that the relationship between organizational management performance and relationship management can be modelled through nonlinearly.

An improved constrained model predictive control approach for Hammerstein-Wiener nonlinear systems

Many industry processes can be described as Hammerstein-Wiener nonlinear systems. In this work, an improved constrained model predictive control algorithm is presented for Hammerstein-Wiener systems. In the new approach, the maximum and minimum of partial derivative for input and output nonlinearities are solved in the neighbourhood of the equilibrium. And several parameter-dependent Lyapunov functions, each one corresponding to a different vertex of polytopic descriptions models, are introduced to analyze the stability of Hammerstein-Wiener systems, but only one Lyapunov function is utilized to analyze system stability like the traditional method. Consequently, the conservation of the traditional quadratic stability is removed, and the terminal regions are enlarged. Simulation and field trial results show that the proposed algorithm is valid. It has higher control precision and shorter blowing time than the traditional approach.

Dynamic Analysis for a SIQR Epidemic Model with Specific Nonlinear Incidence Rate

The article investigates a SIQR epidemic model with specific nonlinear incidence rate and stochastic model based on the former, respectively. For deterministic model, we study the existence and stability of the equilibrium points by controlling threshold parameter R0 which determines whether the disease disappears or prevails. Then by using Routh-Hurwitz criteria and constructing suitable Lyapunov function, we get that the disease-free equilibrium is globally asymptotically stable if R0 or unstable if R0>1. In addition, the endemic equilibrium point is globally asymptotically stable in certain region when R0>1. For the corresponding stochastic model, the existence and uniqueness of the global positive solution are discussed and some sufficient conditions for the extinction of the disease and the persistence in the mean are established by defining its related stochastic threshold R0s. Moreover, our analytical results show that the introduction of random fluctuations can suppress disease outbreak. And numerical simulations are used to confirm the theoretical results.

Application of Nonlinear Predictive Control Based on RBF Network Predictive Model in MCFC Plant

This paper described a nonlinear model predictive controller for regulating a molten carbonate fuel cell (MCFC). A detailed mechanism model of output voltage of a MCFC was presented at first. However, this model was too complicated to be used in a control system. Consequently, an off line radial basis function (RBF) network was introduced to build a nonlinear predictive model. And then, the optimal control sequences were obtained by applying golden mean method. The models and controller have been realized in the MATLAB environment. Simulation results indicate the proposed algorithm exhibits satisfying control effect even when the current densities vary largely.

基于改进哈里斯鹰算法的无人飞行器路径规划

针对无人飞行器三维路径规划问题,提出一种基于哈里斯鹰优化(Harris hawks optimization,HHO)算法的无人飞行器三维路径规划算法。首先根据路径规划代价指标和无人飞行器自身性能,建立路径规划模型确立代价函数和约束条件。接着针对传统HHO算法的不足,引入非线性能量因子来平衡全局搜索和局部搜索的关系,使算法避免陷入局部最小值;引入混沌映射对HHO算法进行初始化种群并对其进行局部混沌搜索,增强算法种群多样性和搜索能力。最后通过仿真实验证明,改进的哈里斯鹰优化(improvement Harris hawks optimization,IHHO)算法可以有效规划出安全的无人飞行器航线,并且能够跳出局部最小值和具备较优的收敛速度。

基于遗传算法的磨削力模型系数优化及验证

在磨削力模型求解问题中,目前大多使用分段计算法或列方程组直接计算各个待求系数,不仅计算量大且其精度也无法保证。另外,传统的回归模型容易陷入局部最优,难以描述非线性关系。为此,将遗传算法引入到非线性优化函数参数优化中,基于外圆横向磨削力模型、平面磨削力模型、外圆纵向磨削力模型等现有的模型数据,开展磨削力理论模型的系数优化方法研究。相关性分析结果表明:通过计算得到的3种模型磨削力的预测精度提高了14.69%~42.54%,且3种模型所预测的法向磨削力的平均误差分别为5.9%、9.13%、3.23%,切向力平均误差分别为6.78%、8.36%、3.69%。经对比知,优化后的模型拟合度较好,模型预测精度显著提高。遗传算法优化后的非线性优化函数GA-LSQ算法更适合磨削力模型的求解,可对磨削力的预测及实际加工生产中的参数优化提供参考。

Global Dynamics Analysis of a Cholera Transmission Model with General Incidence and Multiple Modes of Infection

This paper develops an SIBR cholera transmission model with general incidence rate. Necessary and sufficient conditions for local and global asymptotic stability of the equilibria are established by Routh Hurwitz criterium, Lyapunov function, and the second additive composite matrix theorem. What is more, exploiting the DED is cover simulation tool, the parameter values of the model are estimated with the 1998-2021 cholera case data in China. Finally, we perform sensitivity analysis for the basic reproduction number to seek for effective interventions for cholera control. .

基于Lyapunov-MPC方法的非合作目标近距离抵近控制

针对航天器近距离视线抵近同时存在轨道与姿态机动的非合作目标特定方位控制问题,提出了一种基于控制Lyapunov函数(CLF)的模型预测控制方法 (LMPC)。首先,根据视线坐标系下的轨道动力学方程,建立了满足视线指向要求的航天器相对轨道动力学模型,并推导了期望轨道的解析表达式。其次,利用MPC方法设计控制器进行在线优化控制,并通过纳入基于李雅普洛夫方法的非线性反步控制的显式特征,构建收缩约束式,以确保闭环稳定性。接着,对基于LMPC的控制方法的递归可行性和闭环稳定性进行了证明。最后,仿真结果证明了所设计的LMPC轨迹跟踪方法的有效性和鲁棒性。

具有非线性免疫反应的随机HIV模型的平稳分布

针对一类具有靶细胞生长和非线性免疫反应的随机HIV模型,利用随机Lyapunov分析法以及It8公式证明其存在唯一的遍历平稳分布,得到了存在平稳分布的充分条件.证明中构造了新颖的随机Lyapunov函数,得出了当关键阈值基本再生数R_(0)^(S)>1和病毒繁殖数R_(1)^(S)>1同时成立时,随机HIV模型存在唯一的遍历平稳分布的结论.遍历平稳分布的存在意味着所有个体都可以长期共存.

在线优化可变基的非线性预测函数控制

针对基本预测函数控制只能用于线性系统控制的这一不足,给出基于实用随机NARMAX模型的非线性预测函数控制,采用可克服算法病态的非线性递推最小二乘法进行参数估计,利用在工作点处的动态切平面逼近方法,将实用随机NARMAX模型用线性时变CARMAX模型逼近,使非线性预测函数控制转化为线性模型下的预测函数控制,用线性优化算法求解控制输入,避免了复杂的非线性优化问题,并采用直接极小化指标函数优化算法对可变基函数的加权系数进行在线优化,提出在线优化参数的非线性预测函数控制。仿真研究表明,因算法具有优化可变基函数加权系数和预测函数控制功能,系统具有优良的控制响应。

多函数模型拟合表面张力与浓度曲线的比较

为了更深入地研究表面张力的经典实验,利用Origin软件,采用多种函数模型对表面张力与浓度曲线分别进行拟合,并对每种函数拟合的优缺点加以讨论。其中对数函数拟合数学准确性较高,同时兼具物理意义,更贴切实况。明确了表面张力与浓度拟合的经典实验中以对数函数模型最为适宜。

铁道车辆轴箱振动非高斯特征与分布研究

以对铁道车辆轴箱振动非高斯特征与分布为对象开展研究。基于列车线路轴箱实测加速度信号,提取由轨道冲击引起的轴箱振动特征非高斯信号。使用多个概率密度函数(Probability Density Function,PDF)模型对实测信号进行拟合,并与实测特征信号的经验分布进行对比,评估各模型对轴箱特征非高斯信号的拟合精度。基于W-H非线性变换模型,建立一种非高斯信号模拟方法。利用模拟信号分析非高斯特征对各模型拟合精度的影响。结果表明:列车在行驶过程中具有非高斯特征,当列车经过轨道焊接接头、道岔与波磨路段时,由于轮轨冲击,非高斯特征明显增大,车轮多边形对信号非高斯特征几乎没有影响;基于W-H模型的非线性变换法,可以在保证模拟信号功率谱与指定功率谱基本一致的情况下,进行不同非高斯特征的信号模拟;高斯混合模型能够对铁道车辆非高斯信号较为准确地拟合;随着模拟非高斯信号峭度与偏度的增大,各模型与经验分布的相对误差也会增大,其中高斯混合模型拟合精度相对较高。

Global Stability Analysis of a Delayed SEIQR Epidemic Model with Quarantine and Latent

In this paper, we study a kind of the delayed SEIQR infectious disease model with the quarantine and latent, and get the threshold value which determines the global dynamics and the outcome of the disease. The model has a disease-free equilibrium which is unstable when the basic reproduction number is greater than unity. At the same time, it has a unique endemic equilibrium when the basic reproduction number is greater than unity. According to the mathematical dynamics analysis, we show that disease-free equilibrium and endemic equilibrium are locally asymptotically stable by using Hurwitz criterion and they are globally asymptotically stable by using suitable Lyapunov functions for any Besides, the SEIQR model with nonlinear incidence rate is studied, and the that the basic reproduction number is a unity can be found out. Finally, numerical simulations are performed to illustrate and verify the conclusions that will be useful for us to control the spread of infectious diseases. Meanwhile, the will effect changing trends of in system (1), which is obvious in simulations. Here, we take as an example to explain that.

外伸端板半刚性钢结构连接节点的弯矩-转角智能模型研究

为了寻找一种耗费人力更少、预测效果更好的外伸端板半刚性钢结构连接节点的弯矩-转角(M-θr)关系模型,提出将智能模型引入对该种半刚性连接节点M-θr曲线的预测。首先对现有钢结构梁柱半刚性连接节点M-θr关系经典模型进行了评述,采用其中的幂函数模型对一组试验做了计算并与试验结果进行对比;然后用非线性有限元法对外伸端板半刚性钢结构连接节点进行了计算,并把分析所得M-θr曲线与试验曲线做了比较分析;基于大量试验数据,研究确定了对该种半刚性连接节点M-θr性能影响较大的11个主要参数,并用MATLAB数值计算软件建立了智能模型,对外伸端板半刚性钢结构连接节点的M-θr关系进行了预测,将预测结果与试验值对比。最后发现智能模型不论是定性的曲线变化趋势、还是定量的数值大小,都优于现有幂函数模型和非线性有限元分析,具有更好的可靠性、实用性。所得结论,可为该类半刚性钢结构连接节点M-θr关系研究提供新的思路。